I'm not sure I buy this explanation. Sounds like a lot of work to 'recycle' this bit of parchment. What, was there a shortage of goatskins suddenly? This sounds more like a rather strange 'coverup' for reasons now unknown.
It's Bush's Fault!!!
Imagine if, for everything you want to write down, you had to handcraft the paper. In the case of vellum, that means killing and skinning a goat, tanning the hide, scraping off the hair, further scraping off all the fats, polishing the skin with pumice, bleaching it white if the goat had spots, and trimming it out. Now you have ONE page to write on.
Recycling palimpsets was nearly as common as purging your computer of old documents is today. Chances are, the Archimedes writings were relatively common then, so no one thought twice about reusing the skins.