To answer your question on "how would they know" is that the best way to know is to error on the side of caution. I'm pretty sure Falcon Air found this out the hard way during the Spirit strike. If it smells remotely fishy, don't fly it.

Will there be scenarios where a passenger who was on that Delta flight that is now canceled because of a strike, buys a ticket on United to get where they're going? Sure, is that struck work? No.

We can think of grey area scenarios all day long but it doesn't really apply here. Any cargo that was to be carried out by ABX that day is struck work.