Not so. Carriers do not release any updates directly, nor do OEM's. As was detailed way back, MS gives the OS to the carriers and OEM's of unbranded phones, they do whatever testing they have to to, approve it when they are satisfied and give it back to MS who then deliver it. Firmware updates go through the same process, OEM's test and give it to MS. Only MS has access to the Zune delivery system so when you dont see an update either the carrier has blocked it (as we have seen several times) or the OEM has blocked it. MS technically can push whatever it wants to handsets but they wont so they dont piss off their partners.
So an unbranded phone isnt reliant on the network its on, just the OEM and MS.
Phone updates: process and timing