Yes, that's true--if by 'absolute right' one means that having such a right justifies violation of the rights of others. But the principle that no such right is valid applies just as much to the government as it does to any individual.
However, I assume (or at least hope) that the author of the article didn't mean 'absolute' in that sense. I think he meant 'inalienable,' which means that the right is intrinsic to an individual, not a privilege that can be granted or revoked by others.
The fundamental right is the right to Liberty, which is the right to do whatever is not wrong. In other words, it is the right to do anything that does not violate the rights of others. This right is analogous to the presumption of innocence, where the burden of proof is on those who would claim that someone is guilty of a crime. Similarly, the right to Liberty requires that those who object to the rightfulness of an action prove that it is wrong, by showing it violates the rights of others.
Without the assumption of virtue provided by the right to Liberty, no one would even have the right to present an argument regarding what might or might not be a right. To deny the right to Liberty is to deny your own right to claim anything whatsoever.