My limited perspective from spending time with a private group in residency, their consults generally went out of state -- but, being a pretty substantial group the send out consults were quite uncommon and esoteric, as the practice put a lot of effort into dealing with everything internally and having appropriate expertise, stains, etc. to do so, thus send-outs generally went to specific big names rather than the local academic affiliate (which, well, was also them). My impression was that they were paid directly by the practice. There were only rare patient/physician requests for send-outs, which I believe were processed differently. But, it's been a while.
There was also that case out in the midwest somewhere in which, again if I recall correctly, one state basically said specimens couldn't go across state lines as a matter of routine and be read in another state by a pathologist not licensed in the specimen's state of origin -- but that 'consults' were OK in that consulting pathologists didn't have to be cross-licensed. Think that thread was on here somewhere last year or thereabouts.