It's what is stamped on the movement.
Yeah, I'd have to agree with that statement, with some caveats.
I've collected/studied Girard Perregaux (though not to the point I'd feel qualifying myself as an "expert") since about 1998 & have never heard of a connection between the 2 names.
Quick net searches (and hunts thru my own database of info) don't bring up any references to "George Parrott" as a watch brand, just as an outlaw from the Old West (USA), but there is an auto-fill-in search topic in Yahoo that ties the name to shoes http://www.executedtoday.com/2013/03/22/1882-george-parrott-rawlins-lynched/
@ Mike'sCousinAnthony: can you post some pics of what you have? It would be especially interesting to see if there are any identifying markings on the case-back (inside or outside) & movement (if you can get it open to take pix). OR ... if you don't actually have the watch just give us a reference to it on eBay (like the auction#) if the pix of it I've requested are there in the listing.