In that case, vulnerable populations in gentrifying neighborhoods were no more likely to leave than equivalent populations in non-gentrifying neighborhoods.

For me, the obvious mechanism is that, well, it's true that people who leave may often blame gentrification / increased costs for their departure. But on the other side of it, without gentrification people may still have left, but for different reasons: to get away from crime, to go somewhere with more amenities. It's possible that these two tendencies somewhat balance each other out.