As best I can tell from "the sill-cocks I've met" and your picture, the sill-cock is a typical "threaded outside, solder inside" which has had a PEX fitting soldered in, inside and then crimped. It's not very clear but I think I see the outside male threads on the end of the sill-cock.
This is actually somewhat fortunate for you. When people try to unscrew these on a soldered copper pipe system, they twist the pipe they are attached to, and have more damage to repair. Since PEX fittings act like unions (the fitting turns inside the pipe and ring) you're just spinning, rather than damaging your other pipes.
I would suggest replacing with a PEX-FIP (female iron pipe threads) fitting so you can unscrew the next one. Here, you'll need to cut the copper crimp ring so you can remove the soldered in fitting and the attached sill-cock.
However: It's possible (picture is not great) that you may already have this, and just need to grab on the outside of the FIP fitting, if you have one. That would be a bit further into the hole than you are now, if you have a bronze/brass fitting that male threads from the sill-cock are going into. If I ignore the picture and read the text, that sounds like the case, so you need to grab that, not the crimp ring on the PEX connected to it.