How can ATC clear you for a PRNAV procedure if they don't know your equipment fit ?
That's now how it works, AIUI.
A "PRNAV procedure" can only be a STAR, or possibly a SID.
The huge majority of (for example) high-end bizjets are not PRNAV approved, not to mention 99.99% of lighter GA.
That is why any such airport also has a conventional STAR, and the PRNAV one states on the plate "advise ATC if unable to comply".
The normal ATC procedure is to assume that the plane carries the required equipment.
If ATC at airports that have PRNAV terminal procedures do use the equipment list to decide whether to offer a PRNAV procedure, that would be quite a nice way to do it. But IME that is not how it works.