I've always had action issues with my Fender Jazz, even though the saddles are really low

And talk to another "tech" (and I use the term advisedly, as it does not sound deserved) because anyone who doesn't know that shims serve a valid purpose is not someone I want working on any instrument I own.
Slow down folks. You are judging these techs (seems like there are two) on the basis that one reportedly said the saddles are as low as possible and another tech who said a shim wouldn't do anything. There are a number of reasons why the techs may have said that, all of which may be perfectly valid. There is simply not enough info provided to make any kind of judgment.
 
Everyone seems to be jumping on the idea of adding a shim. This may not be the answer - there is not enough info here to determine what the problem actually is.

The tech said that the "saddles were as low as possible". That may mean "as low as possible without introducing fret buzz", or "as low as possible without choking the higher notes" or something else. Maybe the saddles aren't sitting on the base plate. We don't know what the string height is now, nor the relief. Perhaps there's some un-eveness in the frets, a ski jump. Without knowing those things, it's a wild guess that a shim is needed or even advisable.


^^^This!

OP can you give us some more info.
 
Slow down folks. You are judging these techs (seems like there are two) on the basis that one reportedly said the saddles are as low as possible and another tech who said a shim wouldn't do anything. There are a number of reasons why the techs may have said that, all of which may be perfectly valid. There is simply not enough info provided to make any kind of judgment.

^^^^^And this.
I defer to these wise words.
 
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