I don't know that I've ever seen a Jazz where they were the exact same width.
Me either - not a single one in over 30 years.
Precision basses have a warp in the pickguard (usually either the top side above the neck - inviting a place to store spare picks - or near the output jack).
Jazz basses have a pickguard that never meets the control plate correctly.
It's the Fender way.
The cheapest, most replaceable part goes awry.
I presume that the body gets drilled for the pickguard, according to a template : and the pickguards themselves are drilled in large batches, but are prone to shifting, warping, and shrinkage - so the two never marry up perfectly.
Fender is a utility brand, not a boutique brand.
Consequently, there's a right way, a wrong way, and the Fender way.
It took me 30+ years to finally give in, and buy a Fender (Am Pro II Precision), and you just have to embrace all their quirks.
For example, I'm primarily a StingRay player, and if you look at how Leo Fender did things at Music Man, compared to Fender (things which Fender has steadfastly clung to, for whatever reason) :
Translucent Finishes
Fender will mostly make their bodies from three pieces, with no attempt to match the grain - it's as if they consider it a point of pride that they've successful glued three pieces of Alder together.
Music Man will mostly make their bodies from two pieces, and the grain will be so well matched, the join will barely be visible.
Poly Finish Robustness
If you so much as look at the finish on a Fender, it will develop swirls, and minor surface scratches.
Music Man finishes are about as robust as one can reasonably expect.
Tuning
The combination of the 3+1 headstock design, and the location of the string tree (A & D) on a Music Man, means the a 1/8 rotation of
any of the tuning keys, in either direction, results in an equal change of pitch, sharp or flat.
On a Fender, the 4 in a row, and the string tree location means that if you need to decrease the pitch of the D or G strings, to bring them in tune, you have to significantly slacken them, until they slip under the string tree, before bringing them back up to pitch, with a completely different degree of rotation of the key.
Maple Finger Boards
Since both companies have done away with skunk stripes, and rear mounted truss rods - instead mounting the rod from the front, and then glueing the finger board on :
Fender will will glue a maple finger board on to the neck, with the join clearly visible.
Music Man remove the front of the neck, install the rod, and then glue the exact same piece of wood back in place, to make the finger board with perfectly matched grain, and no visible join.
These are just some of the reasons why I remain primarily a StingRay player, and why Music Man instruments are more expensive than Fender...
But...
A Music Man StingRay is
not a Fender Precision.
A Rickenbacker 4001 is
not a Fender Precision.
A boutique / custom Precision style bass is
not a Fender.
Whilst my Fender Precision may not be absolutely perfect in every single way, it is what it is - which is why we like them in the first place - and I could hardly be happier with it it.
Embrace the Fenderness of their instruments, and the quirks give them character.
dude, we see it --- you pointed it out. but you're making assumptions about those who can't get on with your POV.
the best fender is the FSO someone else makes! 
(e.g., our assemblies! 
)
