IMHO (though a little long) the MIA Fender Jazz just sounds like a bass should sound, to me. On the other hand, I don't think that the money is worth what you get. I picked up a Mexican Jazz bass that sounds exactly like it should. By the time I'm done doing what I want to it, it will add a few hundred bucks to the overall cost (
including conversion to fretless), but it still be cheaper than buying an American one. $480 for a MIM Jazz Bass, $30 for shielding supplies, $80 for a Badass II

, $160 for Fender noiseless pups

, $60 for a basic hard case, and $100 for a REALLY GOOD setup

puts you @ $910. That's about $200 ahead of an American made.
Even then, if your shielding job is good enough you shouldn't need the pups, you could go with a Gotoh 201 bridge for $30 (an upgraded version of the stock "vintage" bridge) and a setup should be more like $50. So you could do it for $670 ($770 if you actually get a Fender hard case).
More than that, for the money spent, there are people here who will argue that Lakland and Shadowsky make a better Jazz than Fender.
Sorry for the can of worms, there.