I had just the opposite experience. I cannot get that sound with anything but a Stingray (or some clone). But I agree with you in that there are lots of Stingray players who would never get a "Denman Sound." Thing is, it's not just the bass, but also in the way the player plays it--attack, fingering choices, strings/gauge, and many other factors. All those factors add up to a certain sound.
I know a lot of people assume that Denman used flatwounds. Not the case at all. I read an interview where he stated he used rounds. It's the Stingray AND the way he plays it. Of course, only Denman can sound exactly like Denman, but like I said, I get his "sound" pretty well with a Stingray or Sterling in the parallel mode and my typical very light touch on the strings. It has gotten to the point that I can't even play those lines on anything else; it just doesn't sound right no matter how I play them.