I'm in Canada and use an unlocked AT&T iPhone on Roger's network without data, had no problem, they even were the ones to install the SIM in my phone. I also had put my SIM from my payphone in the iPhone without any problem before that.
If you are using an iPhone that's not locked to another carrier, how would they know/care what phone you put their SIM into? I guess you'd be beter off giving them a call.