B would not be likely to just suddenly start looking into A's problem. It is likely that the PI discussed the work of each group member with B (at least in general terms) when being interviewed. At weekly group meetings the issues arising for each member would be raised and comments made. Perhaps each member would summarize his work for the benefit of new members of the group. B is more likely to have been thinking about the problem for longer than the day he brought the idea to his PI.

@Trunk: nothing in the question suggests so.

@Trunk I have a hard agree on this. I have been on the receiving, as well as on the giving side of this interaction and I learnt not to do it without invitation. Instead of solving the problem behind the other's back, a suggestion or invitation for collaboration based on the idea would have been a much better action.