I noticed that the TSA is more likely to look at visa pages at international terminals in big airports. SFO immediately comes to mind. I have never seen them doing it at SJC, PDX, SMF or GEG.

Checking a person's immigration status is not the TSA responsibility and they cannot refuse boarding because they suspect you may be out of status, but nobody prevents them from contacting CBP to check you out. Of course, the latter usually do not have that much time to waste on silly and possibly groundless requests.