Apparently when the programmers implemented the system to prevent a character from being thrown while coming in from a snap back or character death, they just gave them a unique unthrowable state, which is cleared if they transition to any other state. Because blocking and being hit are states, an attack on an incoming character changes them to a state without the unthrowable property, with a net result of using a light attack to put them into block stun allows you to throw them afterwards.
This is similar, especially visually, to the MvC2 Guard Break, where you can put an opponent into block stun, let them come out of it, then hit them again. MvC2 had a limit of one action in the air, and the first block consumed that action. Blocking again would have been a second action and, thus, wasn't possible to do again.