The FAA care about safety. If you have anything falling back to Earth you have to prove it is safe. That usually means you have to do some analysis to show your chance of killing someone on the ground is less than 1 in 10,000 (that's the European level, I believe the US level might be tougher).
An easy way to meet this is to land in the middle of the ocean, since there's a lot of space and very few people around, hence SpaceX target the Pacific for the falling second stage.
As part of this you need to identify your expected landing zone, which is then used to warn sailors and aircraft about the risk. But also this is not really enforced - nobody goes out there to check the zone is empty before the launch is authorised, like they do around the launch pad.
But you also need to account for failures in your 1 in 10,000 analysis. So as part of it you look at the probability of something failing and of pushing you off track, and then the risk of killing someone if that happens. Again, this is easy if you are targeting the ocean, since being even a thousand miles off still brings you down in empty water.
So this scenario, where the upper stage fails and comes down in the wrong place, is almost certainly already included in SpaceX’s planning and licensing.
Where the FAA might have questions is whether the probability of failures is correct, or if something has changed in manufacturing to make them more likely.
For SpaceX, obviously, a dodgy second stage is a bigger problem. They need the stage to be reliable for upcoming interplanetary flights and others going beyong LEO. And they'll want to understand what caused it in order to make sure it couldn't happen earlier (which in this case could have been while astronauts were still attached).
So there's a good reason SpaceX are investigating and already announced a pause in flight, and probably a good reason too why the FAA is keeping quiet so far. Behind the scenes I'm sure they're already in contact about the matter.