Just so there's no uncertainty about this: we have never, in 4 years of doing this, told a startup we funded about an idea we read in an application from a group we didn't fund.
The explanation for this is pretty simple: the groups we like, we fund.
That's incredibly honorable of you guys, and thank you! But the explanation I don't buy. If you dislike a group, and choose not to fund them, their idea still might be pretty good. (IIRC, one or some of your essays mention that the greatness of ideas and the groups behind them are somewhat independent of each other).
In this case, what incentive do you have to keep the idea to yourself, and not tell/hint at it to a funded startup?
what incentive do you have to keep the idea to yourself
That we promised to. And in actual fact it is very rare to hear a good idea from a group we don't want to fund. I can only remember being constrained by our policy once, when a group we interviewed had an idea I thought would be useful to Bountii (I think it was).
I would assume that if a VC got the reputation of taking ideas and pushing them to other groups instead of the originators, it would kill their credibility. And without credibility, no one is going to go to them for funding.
The explanation for this is pretty simple: the groups we like, we fund.