I'd say give the names of people who know you, whether they are county residents or not. The Sheriff cannot use that to deny you a permit, and I'm pretty certain that the state law says you have to provide references, but NOT that they have to live in the county in which you're applying.
I'd say they just don't want to be bothered making a long-distance phone call.
I got my non-resident PA permit from the Mifflin County Sheriff yesterday. In the references section I put the names of two VIRGINIA residents. Why? Because I've lived in DC metro for 10 years now, and the people I used to know in Mifflin County don't really know me any more.
Even so, I had my permit in less than 3 hours, but I'm certain the fact that both my family and I know the sheriff helped.