No.
"Inalienable right", like the "right to bear arms", has never meant you get to do anything with it. Free speech doesn't extend to defamation; free expression doesn't extend to murder; freedom of the press doesn't extend to sneaking into the CIA's archives, freedom of movement doesn't apply to jails.
I'm of the opinion that arbitration clauses and non-disparagement agreements of the scope involved in this particular case are unconsionable, because they unreasonably infringe upon such inalienable rights.
(I don't agree - re-read my wording carefully - but some certainly take that position. My point: those who do still tend to take the "but there are limits!" position on, say, home-brewed nukes.)
In each case, though - constitutional right, human right, inalienable right, natural right - the fundamental concept of "sometimes two people have rights that conflict, and society has to resolve this" applies.