You can say that about all the filmmakers of his generation I guess. The difference his relationship with the 'classics' of the field was much less troubled then say that of Coppola or Scorsese. But I'll say it again his command of the language and grammar of his medium is akin to Mozart. No real formal traning. Just a complete natural.
I'm not a big Coppola fan. I'm one of only two or three living people who think that the Godfather was just so-so. Scocese I always thought was hit and miss, but I have to say that I thoroughly enjoyed The Aviator.
In my experience, study and opinion, I've always found movie makers who didn't arrive on the set fresh out of film school always had a creative edge. John Huston comes to mind -- he grew up in a show biz family, but did some living before he stepped behind the camera. James Cameron also did some living and it shows in his movies. And yes, I confess to liking Titanic.
These guys -- and I put Spielberg in with them -- are more academics than artists.