I would consider it a test to see if he can handle assertiveness. That is, if he is fun and easy-going.

The above is correct but this part would depend a lot on how the "no" is delivered:

If he said no, I would think she could consider him either not interested in her enough to part with a few dollars (and too cheap to satisfy a small request), or insecure about his status in the company of a woman.

The real status test is about whether he considers his company to be as valuable as hers. If he complies with the request (without any quid pro quo), then he's ceded her the higher social status -- which was what the question was testing (either intentionally or unintentionally), in the common case.

Declining the request, reversing it (you buy me one), or insisting on a quid pro quo, are the only ways to maintain equivalent or higher status in the interaction (absent an ongoing equal relationship wherein the quid pro quo is assumptive). Also, skillfully handling any of these options raises the observer's estimate of your social coprocessor's power rating as well. ;-)

There are a wide variety of context-sensitive ways to decline or redirect such a request, depending on the situation and level of rapport of the conversation... from the polite to the downright rude, all of which can be functional if delivered with confidence. But certainly, "fun and easygoing" no's are possible.

(For example: pretending to misinterpret the request as an offer, eg. "Oh, yes please. That's very kind of you. I'll have a..", a playful, "Oh? And what are you going to do for me?", or even a humorous, mock-offended and effeminately-voiced, "Hmph! What kind of boy do you think I am? Are you trying to get me drunk and take advantage of me?")

As thomblake points out, "Surely You're Joking, Mr. Feynman"contains his story of finding out this counterintuitive fact - although the specific story involves calling a woman "worse than a whore" for getting him to buy $1.10 worth of sandwiches. She then proceeded to pay him back the $1.10... and then came over later to have sex with him.

In Feynman's second story, he asks “Listen, before I buy you a drink, I want to know one thing: Will you sleep with me tonight?” -- and gets a "yes".

Amusingly, the "Player Guide" (an open-source guide for beginning PUAs) isn't quite so bold - it only recommends asking for a french kiss as the quid pro quo. ;-)

Of course, all of these anecdotes and advice are subject to selection bias - i.e., to the mostly-NT women who show up at bars and ask men to buy them drinks. My guess is that most non-NT women don't ask guys to buy them drinks unless there's either an ongoing quid pro quo (i.e., "I'll buy the next round"), or they've consciously chosen to exploit the social dynamic for financial/alcoholic gain.

tl;dr: a man is generally best-off treating a request for a drink as a test to determine whether he has low enough self-esteem to believe he needs to pay for female company, and an opportunity to display an unruffled and socially-skillful response.