OK, so the Admiral (ret.) is a dumbass. But what’s wrong with the idiom? Sure, the literal meaning is as you say, but the real meaning of the idiom is “destroyed by your own weapon or tactic.”
Even if his advice was stupid, I fail to see how he misused the idiom here, which I took to mean, “make political capital out of their obstructionism, rather than giving them even an inch.”
I am amused by the fact that “petard” in French is the word for “little fart,” which gave its name to the gate-busting bomb.
The idiom’s fine. The problem is the “retired rear admiral” proved himself to be a complete ignoramus by using it to mean “hung up” instead of “blown up.” As a supposed weapons expert he ought to know the difference and at least know what a petard is.