"First anyone that has built an amp and had to tune the input and output understands that impedance matching matters"
that only applies to some of the people that build tube amp from scratch and people that understand how transistors are matched to the load at any given vcc & drive level,
most people that build solid state amps build solder jockey style copying other peoples work & don't understand how they work,
"I have no doubt that the SWR at the antenna was not magically altered by shortening the coax"
you should have doubt because its not magic its physics,
vswr can change with coax length, if the meter said its changed significantly then it DID change with coax length,
"but what good is a perfectly functioning antenna if you can not accurately read the SWR of the antenna system? A meter is of no value if you can not trust it to give you an accurate reading"
you can trust the reading, that is the vswr of the system even when coax length does change vswr,
its not fooling the meter its fooling the guy using the meter, you need to understand what the "system" is and how to minimise the detrimental effects of some of it on your vswr,
if vswr does change with coax length and you don't like it then you need to eliminate the common mode from the braid,
it won't give you a more accurate reading as that is set by the meters basic accuracy but it will stop vswr changing dramatically with coax length,
when your vswr goes down significantly by cutting your coax back a lot it indicates you have cut a faulty piece of coax out OR you have cmc on the braid,
if you had good coax & no cmc vswr should have gone up a little due to reducing cable loss,
"Why do coax companies bother to give us velocity factors if they not of any importance to use?"
velocity factor is important when phase is important such as arrays of antennas fed with a certain degree of lead/lag, or when using coax as an impedance transformer such as 1/4wave inverters or bodgit jumpers between radio and amplifiers that have an other than 50ohm input so the radio sees closer to 50ohm load,
velocity factor is of no significance with regards to vswr changing with coax length unless you get your info from cb forums where that sort of nonsense is posted as if it were true.
Velocity factor determines the electrical length of the inside of the coax and resulting transformer action when the line is mismatched,
You have to wonder why it is that some folk love their bird or mfj but ignore the instructions needed to understand what they are reading,
instead they make sayings up like you are getting REFLECT off the cab or your amp output is not tuned to 50ohms so you have reflect,
just another case of observing an effect but not understanding what's causing,
its karaoki physics, for people who enjoy sounding stupid in public.