First, they can't tell if you're actually receiving the old locals. His account will obviously be set up for them but doesn't mean he's getting them. That leads to the next part:
Wanna bet?
Without knowing where the OP lives today and is "moving" to, he can't get reliable answers. If, using your examples, and I'll presume neither Buffalo nor Phoenix are on Conus beams, he would simply say "We moved from Buffalo to Phoenix last week and I just got my dish re-installed and re-aligned. I'm getting all of my regular programming but I'm not getting the local Phoenix channels. How do I fix that ?? Do you guys need to change something on my account ?? (playing dumb) I guess I thought since I was paying for local channels I'd get them wherever I was at."
Well, if the intent of the move is to get new locals you're SOL (suddenly outta locals). Buffalo goes away and you can't physically get Phoenix. If you are trying to get a CONUS service only offered to Phoenix, it might work but what does the CSR think when you cannot get Phoenix locals? Your receiver knows what channels are hitting your antenna and that can be easily reflected in the location ID number. Now you can either read the correct number (indicating that you didn't move) or play hard to get (and be disconnected).
Now, will his Buffalo channels still show up in the program guide but no programming is available ?? Well, since he really didn't move, yeah, they will. But, does he need to tell the CSR that they don't show up at all or they show up but no programs are available ??