I thought we figured out they can only make that determination on their own dongles.
Not used the 321-PAYG service myself, but on the previous 3 PAYG phone plans I had no problem using it in a data modem, tablet, or USB dongle. Same applies to my current contract SIM. The data modem doesn't even connect the phone line (PS registration only) to the network making it as obvious as can be it wasn't a phone.
I've never seen any network in the UK care what device you put a SIM in so 3's own-dongle-blocking (eww) is already a first for me. But then I used to put 3 SIMs in ancient 2G only phones that didn't even have GPRS or WAP and they still worked.