This article doesn't back up what it claims. The evidence:

“The results suggest that recreational swimming can induce significant modifications in some skin biophysical properties related to skin hydration.” This abstract, "Variations of skin biophysical properties after recreational swimming," was published this month as a full paper in Skin Research and Technology.

In this article, Sophie Gardinier et al. describe a study where skin hydration, skin pH, transepidermal water loss (TEWL), skin temperature and sebum casual levels were measured at 0, 4, 24, 48 and 72 hr after the start of the study. The study was repeated a second time but after the subjects had been swimming for 1 hr between the first and second measuring point. During the control period, none of the skin parameters showed any significant variation over time on all body sites that were measured. In contrast, during the swimming period, significant changes were found 1.5 hr after swimming for skin pH (increased) and sebum casual levels (reduced on upper chest but not on the forehead), while TEWL and skin temperature remained unaffected. From the next measuring point (t = 24 hr) onwards, all changes had disappeared.

This might be evidence against long showering, although shower conditions are not pool conditions. There's a difference between being submerged in water and having it fall on you. And that is after an hour and a half, which is far longer than what people consider to be long showers anyway.

But, this is most definitely not evidence against hot showers, or even frequent showers. This is only evidence for harm being done in a single long submersion in water.

Furthermore, if you go to the study they site, the sample size is 9, and they only have female subjects.

They address the chlorine argument:

But how does this scientific backing help a parent in a "shower battle” with their teenagers? First of all, these teenagers argue that their shower water is not chlorinated (true), to which I argue that the water in our city is hard, which increases the irritancy effects of water.

But that only applies to some cities, and the mineral content is still different.