Because their arguments couldn't work unless they claimed it.
Just to be clear: the claim of self-evidence was not applied to the rights themselves, but the fact that they were granted by a Creator.
This is a very important point: those principles held out as unalienable rights, cannot be derived from first principles, nor from observation of the natural world.
In many or most respects, among humans or among any other combination of species, the world seems to operate very nicely on a principle of Might Makes Right.
So how does one arrive at the opposite pole that people, individually, have rights? One invokes a Creator Who makes a rule like that. (As it happens, I believe this to be true.)
Ayn Rand's philosophy collapses on this point, in that she attempted to derive the unalienable rights apart from a creator; but she failed. In effect, she was forced to put herself, and her own assertions, into the same Creator role that she had so stridently rejected.
The bottom line, though, is that those unalienable rights don't simply spring up like laws of nature. They have to come from somewhere -- to be asserted.
Yes, the primary precepts are axiomatic, principles that one cannot not know, such as "avoid evil."
The secondary Natural Law precepts build on the primary, by man's right reason, such as the pursuit of happiness.
Regarding the natural world, the laws of motion and calculus discovered by Sir Isaac Newton were regarded as Natural Laws, a reflection of Eternal Law, discovered by man. This concept went well into the 19th century when what we call physics professors today described themselves as Natural Philosophers.