In the nose of the rocket is a little thing called a “guidance system” It can change course anytime. This whole thing is stinky cheese. The reason NorthCom can tell us with certainty that there is no threat to the US is because they know exactly what happened. They just are not telling us.
That and the fact that the gov has no problem lying to the public. This is the kind of thing they have kept secret all along. Even if it came from a hostile as a warning they could say honestly that there is no threat. The caveat is that there is no immediate threat as it was obviously a warning (saber rattling).
But your hunch is the most likely scenario. It was ours and for some reason they don't want to own up to it.