Remember the whole thing about Musk buying Twitter? One if his reasons for doing so was because he believes Twitter is "censoring" conservative speech. But Twitter is a private company, running a private service, so your strict government-focused interpretation of free speech clearly wouldn't apply.

Musk has stated in his own words that he is a "free speech absolutist", and given his complaints about Twitter it seems that his interpretation of that is not limited to government censorship, but all censorship.