"the Prime Directive is not just a set of rules. It is a philosophy, and a very correct one."
(i.imgur.com)
It's applied to other civilizations pretty regularly.
The most cut-and-dried one off the top of my head is Sisko citing the PD when declining to help Tosk in "Captive Pursuit".
The Prime Directive and the rules governing first contact overlap, but they are distinct.