Yes, AT&T seems to be an issue.
My understanding is that Tracphones can use any of the major carriers; it depends on the phone and vendor (Walmart, etc.) This applies to "SmartTalk", MyFamilyMobile, etc.
It is difficult, but not impossible, to ascertain which carrier a specific tracphone will use. For example, I used to have a SmartTalk tracphone that worked intermittently at Sheepscot and up and down the line; I think it was using 2nd-tier Verizon (which means that you get bumped for regular Verizon customers when necessary.) My current phone (which recently got damaged and needs to be replaced, hence the question) uses MyFamilyMobile and AT&T as the carrier; it is completely worthless at Sheepscot or anywhere on the RR.