There's a vast difference in bikeshare bikes that have hundreds of different people who don't own them riding them each week and a personal bike. I use bikeshare in NYC, London, and elsewhere regularly and have never had a problem but I know that problems do occur.

My info on disk brakes comes from mechanics and bike builders in The Netherlands, Denmark, and Motivate (NYC Bikeshare). They've all said that they'd like to use disk but all consistently say that they're not as reliable as roller or coaster and they don't want the problems.