Verizon and Sprint do have their own branded phones, however, they are technically made by smaller phone manufacturers like UTstarcom and Pantech.
MOTO pretty much chooses what phones they want to introduce to nextel and then nextel picks which ones they like.
That's the relationship between any carrier and phone manufacturer. The carrier doesn't tell the manufacturer what to make.
If someone says "nextel phone", anyone familiar with the carrier will know that the phone is made by Motorola because the two are so closely related. I'm not arguing the fact that Motorola creates the phones to be used on the Nextel network. The terminology is just not worth getting anal about.