There are station retrans, and then there are cable/MVPD program deals. DirecTV falls under the latter. Just like Comcast, Charter, Fios, and Dish, DirecTV pays for the network programming on their cable satellite/stream. That payment, which has been a major bone of contention, includes ESPN the second-highest program fee next to Fox News. Not only is DirecTV unhappy about Disney looking for an increase in ESPN and Disney Channel, but they've become increasingly butt-hurt over having to pay these escalator fees to carry programming during rampant cord-cutting. Then Disney adds insult to injury by competing against cable and DirecTV by streaming around cable/satellite. Essentially, cable companies are upset because they have to buy Disney programming staring down the barrel of a gun with Disney also competing against them.
Regarding local ABC stations carried via DirecTV being blocked, that's because the beef is with DirecTV.