It fits as a "total war" mentality essentially. Delivering food to a city is supporting a siege. So is paying protection money supporting an armed group of criminals. Technically right but a matter of nuance. It may be effective in some cases but like nearly anything assuming automatic morality is a way to leap off the slippery slope.

Even the advocates don't take it literally usually because of how barking mad that would be in a "strangle infants for not supporting the cause" way. But that isn't special because any philsophy can be twisted into something horrific.

I suspect its popularity is more for the memetic effectiveness than a deep philosophy - regardless if it is right.