We'll need a basketball lawyer to weigh in (
@stamfordhusky , where are you?), but I don't think the bolded statement above is necessarily correct. I think you meant to say that "if it is seen by an official, it is
at least a common foul." Officials can call the common foul and then review the replay to determine whether it warrants an upgrade to "intentional".
By the way, "intentional" doesn't mean what it sounds like -- it doesn't require the official to determine that the player intended to hit the opponent in the head, only that it was careless and not the result of a normal basketball play. The term "flagrant" (used in the WNBA) would be more descriptive than "intentional". (Never mind that truly intentional fouls by the losing team near the end of the game, for the purpose of stopping the clock, are never called intentional and normally do not involve any risk of injury to the player who is fouled.)
However, you are correct that if the refs do not see or call the contact to the head during live action, they may still review the play to see if it warrants a flagrant/intentional foul. (This will usually happen because the player who receives the facial hit is on the floor in obvious discomfort.) If the replay results in a determination that the foul was flagrant/intentional, then it can be called and free throws can be awarded, BUT if it does not rise to the level of flagrant/intentional, the officials cannot retrospectively call a common foul even though that's what it was.
Is this correct? Is it comprehensible?