So you're saying that a standard Stingray can capture the jazz bass type tone? A precision bass type tone? I'm sorry but if you're talking about a standard, single pick up Stingray, they aren't capable of that. You may be able to get close with a double pickup Stingray (which I assume is what you mean), but it's still got its own character that is undeniably Music Man.
I used to play a Music Man (single pick up) for many years and I ended up giving it up for its lack of presence in a mix. Too thin sounding to really fill out the deepness I was looking for in many songs (but I realize everyone's needs are different). There is certainly no way that it was capable of sounding like anything but a Music Man. The unique type of pick up, pick-up placement, and electronics design of a standard Stingray is going to sound unlike any other design. That's sort of why they were invented; to fill a tonal range that no other bass could hit. But for me, personally, it doesn't work for most things.
I'd say the most versatile type of tone is a double soapbar design with a flexible preamp. They can usually cop a very close precision sound if the neck pickup is in the right place and they do the "jazz bass on steroids" very well. As well as a variety of other things if you incorporate coil tapping.
I, however, am a bit of a purist so I have jazz, precision and soapbar style basses because I don't hear any of them as being able to hit each other's tones exactly.