I will quote at length here.

3. The Argument
1. Most sweatshop workers choose to accept the conditions of their employ ment, even if their choice is made from among a severely constrained set of options.18
2. The fact that they choose the conditions of their employment from within a constrained set of options is strong evidence that they view it as their most-preferred option (within that set).
3. The fact that they view it as their most-preferred option is strong evidence that we will harm them by taking that option away. 4. It is also plausible that sweatshop workers' choice to accept the condi tions of their employment is sufficiently autonomous that taking the option of sweatshop labor away from them would be a violation of their autonomy. 5. All else being equal, it is wrong to harm people or to violate their autonomy.
6. Therefore, all else being equal, it is wrong to take away the option of sweat shop labor from workers who would otherwise choose to engage in it.

5. Challenges to The Argument
I will discuss three potential vulnerabilities in The Argument. One potential vulnerability centers on premises 1, 2, and 4, and stems from possible failures of rationality and/or freedom (which I will group together as failures of voluntariness) in sweatshop workers' consent. The second is located in premise 3, and derives from a possibly unwarranted assumption regarding the independence of a potential worker's antecedent choice-set and the offer of employment by a sweatshop. A final criticism of The Argument is centered on the conclusion (6) and holds that even if everything in premises 1-5 is true, it nevertheless ignores a crucial moral consideration. That consideration is the wrongfulness of exploitation?for one can wrongfully exploit an individual even while one provides them with options better than any of their other available alternatives.
a. Failures of Voluntariness
The first premise states that sweatshop workers choose the conditions of their employment, even if that choice is made from among a severely constrained set of options. And undoubtedly, the set of options available to potential sweatshop workers is severely constrained indeed. Sweatshop workers are usually extremely poor and seeking employment to provide for the necessities of life, so prolonged unemploy ment is not an option. They lack the education necessary to obtain higher-paying jobs, and very often lack the resources to relocate to where better low-skill jobs are available. Given these dire economic circumstances, do sweatshop workers really make a "choice" in the relevant sense at all? Should we not say instead, with John Miller, that whatever "choice" sweatshop workers make is made only under the "coercion of economic necessity" (Miller, 2003: 97)? And would not such coercion undermine the morally transformative power of workers' choices?
I do not think so.38 The mugging case discussed in section two shows that while coercion may undermine some sorts of moral transformation effected by choice, it does not undermine all sorts.39 Specifically, the presence of coercion does not license third parties to disregard the stated preferences of the coerced party by interfering with their activity. After all, one of the main reasons that coercion is bad is because it reduces our options. The mugger in the case above, for instance, takes away our option of continuing our life and keeping our money, and limits our choices to two — give up the money or die. Poverty can be regarded as coercive because it, too, reduces our options. Poverty reduces the options of many sweatshop workers, for instance, to a small list of poor options — prostitution, theft, sweatshop labor, or starvation. This is bad. But removing one option from that short list — indeed, removing the most preferred option — does not make things any better for the worker. The coercion of poverty reduces a worker's options, but so long as he is still free to choose from among the set of options available to him, we will do him no favors by reducing his options still further. Indeed, to do so would be a further form of coercion, not a cure for the coercion of poverty.40

[C]40. See Radcliffe Richards, 1996: 382.
[Radcliffe Richards, Janet (1996). Nepharious goings on: Kidney sales and moral arguments. Journal of Medicine and Philosophy 21 (4):375--416.]

[C]74. For instance, in 1992, the United States congress was considering legislation known as the "Child Labor Deterrence Act." The purpose of this act was to prevent child labor by preventing the importation into the United States of any goods made, in whole or in part, by children under the age of 15. The Act never received enough support to pass, but while it was being debated, employers in several countries where child labor was widespread took preemptive action in order to maintain their ability to export to the lucrative U.S. market. One of these employers was the garment industry in Bangladesh. According to UNICEF's 1997 "State of the World's Children" report, approximately 50,000 children were laid off in 1993 in anticipation of the bill's passage. Most of these children had little education, and few other opportunities to acquire one or to obtain alternative legal employment. As a result, many of these children turned to street hustling, stone crushing, and prostitution — all of which, the report notes, are much more hazardous and exploitative than garment production (UNICEF, 1997: 60).
["Sweatshops, Choice, and Exploitation"
Matt Zwolinski
Business Ethics Quarterly, Vol. 17, No. 4 (Oct., 2007), pp. 689-727
Published by: Philosophy Documentation Center
Article Stable URL: http://www.jstor.org/stable/27673206]

From the UNICEF report:

An Agreement In Bangledesh
An important initiative to protect child workers is unfolding in Bangladesh. The country’s powerful garment industry is committing itself to some dramatic new measures by an agreement signed in 1995. The country is one of the world’s major garment exporters, and the industry, which employs over a million workers, most of them women, also employed child labour. In 1992, between 50,000 and 75,000 of its workforce were children under 14, mainly girls. The children were illegally employed according to national law, but the situation captured little attention, in Bangladesh or elsewhere, until the garment factories began to hide the children from United States buyers or lay off the children, following the introduction of the Child Labor Deterrence Act in 1992 by US Senator Tom Harkin. The Bill would have prohibited the importation into the US of goods made using child labour. Then, when Senator Harkin reintroduced the Bill the following year, the impact was far more devastating:garment employers dismissed an estimated 50,000 children from their factories, approximately 75 per cent of all children in the industry. The consequences for the dismissedchildren and their parents were not anticipated. The children may have been freed, but at the same time they were trapped in a harsh environment with no skills, little or no education, and precious few alternatives. Schools were either inaccessible, useless or costly. A series of follow-up visits by UNICEF, local non-governmental organizations (NGOs) and the International Labour Organization (ILO) discovered that children went looking for new sources of income, and found them in work such as stone-crushing, street hustling and prostitution — all of them more hazardous and exploitative than garment production. In several cases, the mothers of dismissed children had to leave their jobs in order to look after their children. Out of this unhappy situation and after two years of difficult negotiations, a formal Memorandum of Understanding was signed in July 1995 by the Bangladesh Garment Manufacturers and Exporters Association (BGMEA), and the UNICEF and ILO offices in Bangladesh. The resulting programme was to be funded by these three organizations. BGMEA alone has committed about $1 million towards the implementation of the Memorandum of Understanding. Under the terms of the agreement, four key provisions were formulated:
• the removal of all under-age workers — those below 14 — within a period of four months;
• no further hiring of under-age children;
• the placement of those children removed from the garment factories in appropriate educational programmes with a monthly stipend;
• the offer of the children’s jobs to qualified adult family members.
The Memorandum of Understanding explicitly directed factory owners, in the best interests of these children, not to dismiss any child workers until a factory survey was completed and alternative arrangements could be made for the freed children....
[http://origin-www.unicef.org/spanish/publications/files/pub_sowc97_en.pdf. Panel 12; pg.60.]

Conclusion:
The argument that closing sweatshops leads to prostitution appears a valid one, as according to a 1997 report by UNICEF, it happened once in Bangladesh. According to that same report, provisions were established to prevent it from happening again (in Bangladesh).
(Personal opinion: There's too little evidence to determine whether the argument is actually sound. It happened once, though, and I find little reason to assume conditions in other countries are so different than they were in Bangladesh. However, thus concluding that sweatshops are good would be a misstep. One should rather conclude that if one is to close a sweatshop, provide alternative employment or enable and equip the workers to find their own alternative employment.)