Just an update, hope this all makes sense.
I am at my mom's this weekend and my aunt (who lives next door) also got the same call from "Dish", but she doesn't actually have dish anymore. My Mom said they told her she needed to pay the $200 or they would shut it off. My Mom said she wasn't going to pay it, so they logged in to her account and paused her service.
SO, my understanding is that these scammer people did have her account info, and they logged in and paused her account, trying to get her to call them back and pay the $200.