Hello and welcome!
That is definitely an old Police model. G-2 steel was used by Spyderco sometime around the timeframe you describe, and I think the very old Police models did not have the rivets. Also, in the olden days, there were less counterfeiters making fake Spyderco products. And I don't see anything obviously fake about it, although Photobucket keeps covering the photos with a large pop-up complaining about my ad-blocker and I can't get a good look at them. It's probably genuine. Very cool old knife!
EDIT: I found this quote about G-2 steel:
"When we first began making knives in 1981, we used a steel called Gingami I. It was the best available stainless blade steel in Japan at the time. (It's called Gingami I which means "silver paper" which was the color of the paoer in which the steel was shipped). We wanted to put the name of the steel on the blade, but the maker had "giri" (obligation) to another manufacturer and wouldn't allow us to use the name Gingami I. There was no US equivalent to the Hitachi steel, but we had to make some kind of designation because we were payng a premium for the steel and had to justify the higher cost to our customers. We decided to call the Steel G2 (which stood for "good sh*t also") and offered the chemistry of the steel in our literature."