I'm not too sure but I think it used to be that 20BB was the minimum BI at alot of sites. There were alot of SS grinders/abusers who would double up and leave tables and wait until they can buy in for 20BB again. It made alot of people unset and poker sites
increased the minimum BI to 40BB. I could be wrong but I vaguely recall something like this happening though I wasn't really playing back then so I wouldn't know for sure but I'm pretty certain this happened.
So yea, some people are proficient at playing with those stack sizes. Ultimately, while medium stacks are not as easy push/fold as short stack play, they both look to exploit big stacks that cannot adjust to their presence. And well if they are serious about it and can't exploit you or anyone else on the table, they'll probably just leave and find a juicy table.