I work at $BIGCO, 3 days on, 4 days off, 2 of which I usually spend learning tech and non-tech related things and/or working on side-projects I'm interested in.
I think there are multiple reasons why I was allowed to do this:
A) I'm working on a stable, long-term project. So there were no objections by colleagues that this might impede short-term progress (and, as a side note, I think I'm far more productive now than previously).
B) My manager is a reasonable and kind person. I know other managers at $BIGCO who, I'm sure, would have objected.