Oh, boy. The speculation and armchair telecom experts are going to have a field day with this one.
I'll tell you all what I was taught in journalism school: Check your sources for claims and don't jump to conclusions based on incomplete data.
I agree, which is why I posted a link to DISH's release and not multiple speculative articles out there. 
Several analyst's take as they peer into their crystal balls.
Dish deal terrible for AT&T
https://www.fiercewireless.com/operators/analyst-dish-deal-terrible-for-at-
Does Ting still offer Verizon network or are they switching to AT&T?
Currently, Ting continues to offer its' X3 (TMO) and V1 (Verizon) SIMs. The latter must be requested from support. Ting SIMs sold publicly are X3 (TMO) SIMs.
For the future, DISH's deal with AT&T suggests AT&T will be the primary but not necessarily the exclusive coverage option for DISH owned brands (Boost, Republic and Ting). Time will tell.
Is Ting customer service still as responsive as they were before being bought out?