That's funny, I've had the complete opposite experience - people are known nationally within their specialty area and no one knows anyone locally unless they overlap in their work. Pretty much any psychologist I talk to at our usual conference knows both my mentors. Virtually every internship site I'm looking at has someone on faculty who knows one or both, has collaborated with them at some point, etc. Heck, I've met many of them myself, some have come to visit our lab, etc. In contrast, many of the folks in the local VAs have no idea who they are.
I think there may be differences in institutional culture. For instance, I haven't been to a regional or state conference since undergrad - we really only attend national/international conferences. Networking is done nationally (something I'm banking on helping out when I apply for internships!). Not that you ignore people doing similar work just because they are local, but in my experiences the focus is generally on getting national recognition and who cares what the person down the road thinks.
My take is that there are a fair number of "big names" within specialty areas that help when doing things within that area (internship and post-doc certainly, probably less so for faculty jobs). Then there are the cross-field "big names" where any psychologist worth their salt is going to know the name immediately (e.g. Barlow, Lilienfeld, Joiner, etc.) that will likely help across the board.
As others have said though - CV seems to trump most of these things. These things may provide an "edge" to get you looked at if you otherwise wouldn't, but from what I have seen these things don't weigh in too heavily beyond that.