*Absolutely no right* means "lack of any right whatever, lack of any right at all". *Absoutely* modifies *no* and characterizes the **lack** of right as *absolute*—the lack is unqualified under any circumstance.

*No absolute right* means "lack of an absolute right". *Absolute* modifies *right* and characterizes the **right** as *absolute*—the right is unqualified under any circumstance. ***No** absolute right* implies that some sort of right exists, but any right that exists may be qualified under some circumstances.

From a purely linguistic point of view, the State's argument is without merit. (This does not, however, preclude the existence of statute or case law which overrides the linguistic point.)