Reminds me of how I thought I broke my 70-300 IS USM forever. Got some dirt on the rear element (because it's quite close to the rear of the lens), so got Eclipse and tried to clean it off. Left haze marks all over the lens and in a pattern which suggested that the coating itself was coming off! Multiple cleanings and a change of fluid did not help either, as did wiping it with a Pecpad. I was about to become a filter convert forever (as if I wasn't before) as lens coatings truly seemed to be every bit as fragile as made out to be.
A while later in despair, figuring I would be visiting Canon's service center the next day to ask for a rear element replacement, I guessed I had nothing to lose since the element was f'ed anyway, so I grabbed a Pecpad and scrubbed it really hard.
Amazingly the haze finally came away. Took a lot of scrubbing, like the amount of elbow grease you'd use to scrub a dirty sink and about as much pressure, but the 70-300 IS was restored to as-new condition and has gone on to take many more nice pictures. So the coating *IS* very tough indeed. I am impressed. However, I'm still going to use filters. So what if it's only psychological? I *AM* precisely buying them because they make me feel more comfortable. It's for the owner, not the lens. Works for me.