I have an iPhone SE model #1662 which works perfectly under the BYOD program. I bought it from ATT and used it on their prepaid GoPhone service for long enough to get it unlocked. I then switched to TMO, and now it is on XM. It took less than half an hour to go through the entire process at the XM store. The first question the CS person at the store asked me was "is this a Verizon phone". The model 1662 is the ATT/TMO/Verizon variant, so I said "yes". I believe that what they are trying to determine is whether your phone compatible is with Verizon, but I suspect that some CS folks think this means that you needed to buy the phone from Verizon. This is not true. An iPhone SE model 1723 will not work with XM, a model 1622 will work; it must be carrier unlocked.
If you don't know someone who will loan you their Verizon nano SIM for 2 minutes, you can find "no service" Verizon nano SIM cards on eBay for $5 or less. If your iPhone is unlocked, restarting the phone with even a "no service" Verizon SIM installed will download the Verizon Carrier Update to your phone. Then, if it becomes an issue at the XM store, you can show the CS person that you have the Verizon firmware on the phone which may help proving that it is a Verizon phone.