AA has been making this announcement and enforcing this policy since soon after 9/11. Just because a crew publically blames it on TSA does not mean that it is, in fact, a TSA mandate.
Frankly of all the TSA rules, this one, if actually from TSA, seems the least "Gestapo" of any of the one we've discussed in this forum. Too many people milling around the cabin makes it harder for the cabin crew to keep tabs on what is going on. It makes sense to me to limit people from doing this.
Also, I highly doubt TSA is concerned with economy passengers using premium cabin lavs.