HR don't validate resumes before you get a call back; that would be super-inefficient. As a hiring manager of course experience at the big co's catches my eye, but unless you're hiring there as well (and most of us are not) I actually figure I can't get them interested anyway, so don't pursue these people. Someone who claims deep technical or experience or people management though? I'm totally going to jump at the chance to talk to them asap, even if I've never heard of their current company.