What could cause a wall mounted sink to fail?
You can see the angled mounting bracket hanging down under the sink. The bracket is what holds the sink firmly on the wall, the lower holes  in the sink are for keeping the bottom of the sink from being pulled away and up from the wall once it is lowered down onto the bracket. The top holes have nothing to do with the mounting of the sink. 

The bracket failed, probably because it was not screwed into structure ( studs ).

We can not see inside the wall to say exactly why the screws pulled out. 

The bracket must be attached to studs or usually to a block that is run between the studs. 

The bracket is essentially a french cleat, the back of the sink is cast so that is slips down onto the bracket. The bottom holes in the sink are just to secure the sink and keep it from being lifted up and off the bracket. Adhesive or caulk have nothing to do with keeping the sink on the wall. If some thought that was the case they were mistaken.

The bracket holds the weight of the sink.