"Liability" isn't really how we try to see things in aviation. While it's true that it's ultimately considered the responsibility of the truck/plane to visually confirm that crossing the runway is safe, refuse unsafe commands from ATC, and comply to the best of their ability when ATC says "stop" at the last second, we can't stop our analysis there if we want to prevent this from happening in the future, because unless things change someone will make this mistake again in the future. Telling people not to make mistakes isn't going to help at all; it's obvious, and no one wants to cause an accident. The error is just the last step in the process that led to the collision.

I don't think the ATC is at fault here. If they were put in a difficult situation and responsible for too much at once, I'd view that as a leadership bug, not their personal fault (or anything they should be held liable for). The weak links imo here are the firetruck driver and whoever that ATC reports to directly (i.e., there shouldn't have been an opportunity for this to happen—that's an executive failure, whether they want to take ownership or not).