What the DoJ is really saying is "Folks, we don't feel obliged to support the AA/BA alliance in it's present form but if you figure out "the price (in slot reductions) you're prepared to pay, we may change our mind".
As you correctly state, the DoT has jurisdiction over this alliance.
It's difficult to believe the claims of Delta, Continental and Northwest that they absolutely need access to LHR. It's not as if they have a connecting hub they need to plug in to. And as everyone knows, LHR is about as bad as LGA was until the Port Authority stepped in.
Smart folks go to Gatwick and jump on the express train to Victoria.
Why would DAL, CAL and NWA not have a problem with their euro hubs but have a fundamental problem with AA/BA?
It's called competition, And DAL,CAL and NWA don't want it if they can avoid it.