As someone who has done that same mission (not SF, but a cobbled together team under an SF guy) what you all don't realize is that the "support role" means you're driving around in their vehicles, walking alongside them on patrols, and doing basically everything else except kicking in the door yourselves. Hell we had one KIA and three Purple Hearts (including my own) which were picked up as "support".I am pretty sure that even our own govt. admitted that Special Forces were in Gaza, but only in "support roles" and helping in the search for hostages.
If any of our special forces were hurt in this process, or if they hurt anyone else, is probably something we will never know. Or at least not know unless someone spills the beans on it.
Any American SF operating in a "support role" would be exposed to the same fires that the unit they are supporting is.