Sort of. I don't think they establish what Al is saying. Grohl still wanted Goldsmith to tour in support of the record and to stay in the band; it was Goldsmith who chose to quit. To me, the documentary did not establish that Goldsmith wasn't a good enough drummer (clearly Gil Norton thought so). Grohl's objection to what Goldsmith played on the record wasn't specifically "not competent", it was:
"There was the constant feeling that, whatever song you were playing, Dave had (the) drum part for it, already, in his head or whatever."-- Goldsmith
"When I've written a song... (pause)... I have kind of a clear idea of where the basic roots accents should lie. It's a fancy way of saying 'I know what the drums should sound like, in my head, as I'm doing this thing. That's not necessarily fair, to say that, (as you're) collaborating with other musicians." -- Grohl
"I think that William played the best that he could, and that sometimes it was great, and sometimes it wasn't. If I listen to a song, and I don't think it has the thing that it needs, it's not necessarily gonna get past me, and get on an album." -- Grohl
"The conversation I eventually had with William was, I really wanted him to stay in the band, and I really wanted him to be the drummer. But, I was gonna play drums on (The Colour and the Shape). It's a tough thing to talk about, because I know William will never forgive me for playing drums on that record, and I wish things were different. But, um... I felt like this was what I had to do in order to make this album happen." -- Grohl
So Grohl thought the album would be better, and I'm sure all the record company lizards thought it would sell better, with his drumming on it. Clearly true. There's a huge gap between Grohl and Goldsmith's talent, to the point Grohl wanted to write Goldsmith's parts. There's much less of a gap, if any, between Hawkins and Grohl as drummers, and that's where I'm curious as to how much input Grohl has on the drum parts nowadays. I think @Lurch probably nailed it, it was probably "more then, less now". I am guessing that Hawkins was all along able to compose something approaching what Grohl wanted and after 20 years, can just about do it in his sleep. And those two are (apparently) close enough that it was probably always a different story when/if Grohl wanted something changed.