It's not a problem. Those newscasts used to air later in the morning (and do in markets where local morning news starts later). They can either slide them back to 4 am (thus cutting off 30 minutes of America This Morning on ABC or Up to the Minute on CBS....and, really, they're all network news programs anyway). NBC 10 would simply need to drop a repeat of Access Hollywood.
Think it through...do you really think "America This Morning" is as big a deal to ABC...or channel 6...as World News, or even Good Morning America? They're not the crown jewels of the lineup, they're good filler material. If Disney, to continue the ABC example, can generate more money with ATM at 4 and Action News at 4:30, guess which one will win?