How often have you heard these claims? Too often, I think. However, I contend that nobody is completely self taught. As for playing by ear, I should hope so!
Of course you might think that playing by ear is as silly a statement as 'painting by eye'. And perhaps it is. But at the same time it's true. The artist paints by seeing both what's on the canvas and what's in the mind's eye. In the case of music, all good musicians play by ear -- listening to the sounds on stage and in their heads, and trying to bring the two together.
As for 'self taught', don't get me started ... oops, too late. People learn by attending to ‘data’ and then assimilating it. Once acquired, the data can be used in a variety of situations. And where does this data come from? Everywhere. One way to streamline the process is to hire someone who's already done a lot of assimilating and get them to show you the way, i.e. a teacher.
But whether you take formal lessons or not, you are still studying. Every time you listen to music, watch another drummer play, or talk shop with a drummer or musician friend, you are taking a lesson of sorts. The only difference is that the lessons come at unexpected times and in an un-planned order.
When I was an aspiring young drummer, I spent more time at jazz clubs than I ever did with my teacher. At clubs, I could hear what it sounded like, and I could see how it was done. I built most of my drumming 'chops' that way. I'm also something of a visual learner, so going to see an ace drummer in action was, for me, the equivalent of attending a scholarly lecture. It was also cheaper, a lot more fun, and I never once fell asleep (I can’t say the same about some of the lectures I’ve attended). Plus I sometimes got to hang out with the ‘prof’ after class.
So the next time someone says, "I'm completely self taught; I play by ear", I just might respond with, "Ya, me too! And I took lessons."