Exactly this. You have a much smaller chance of rolling over something sharp on a 700x25C tire, but that tire is rock hard being inflated to 100-110 psi. Its also very thin and likely has almost zero tread articulation. A piece of glass will slice deeply right into it. A fat tire running at 12 psi on the other hand - and lets say you are running a 30 tpi tire casing as I try to do on my commuter tires - that tire has a shot at conforming over a sharp object. Even if the tread is cut, it may not get all the way thru thanks to the thicker 'armor' of the hugely-more-substantial tire casing.
To further muddy the weaters: I have found that front tire flats are effectively nonexistent on fat tire'd urban commuters. Likely because of the points made above (not even a cut, though). the back tire is a different story. Before I seem to have cracked the code with a modern uber-sealant, I had not infrequent flats in the back... sometimes sealed by my Sealant 1.0 (Slime) and sometimes too much for it to handle. But either way... we're talking nails, more nails and bits of steel. How did I miss them with the front and not the back? Simple: I didn't. The front is protected as described above. It rolls over, say, a nail and for lack of a better term just gives it a bear hug and keeps rolling. But... it also doesn't let go instantly. That nail is held onto for a fraction of a second, which means it goes airborne. Straight into the back tire.
So, on occasion while I was still riding fat tires I would hear the occasional hissHissHiss which would be my signal to jump off the bike, grab the needlenoses in the bag on my handlebars, pull the nail, then jump back on and ride, letting the sealant do the rest. Over the last year my puncture frequency simply went away. Now that I am running 'flatless' skinnier tires I haven't had any sort of incident since January 2021 at least, which is when the Bullitt became my daily driver. I crossed 2300 miles on it over the weekend.