+1 to that. If you want intros to VCs then identify target companies, then mine LinkedIn to find out who you know who knows people there. If you're not just starting out in your career, you're likely to find a bunch of avenues. And they'll probably lead to meetings. This would have been harder in 2008, of course, so I understand that it wouldn't have worked for the GP. But for people starting now it should work.
OTOH as the OP says, the chances of getting funded by anyone you meet that way are vanishingly small. But if you do truly impress anyone, they are quite likely to introduce you to other people. And those people can wind up being either investors or introducers to investors. Think of the LinkedIn mining as a way of bootstrapping your VC network.