"If it does turn out to be an antenna problem, am I within my rights to tell them to take the new stuff out of the car, put in my old tuner which I have at home, and refund me?"

Yes.

Heres a self test...Go to Your local auto parts store.
Buy a cheap antenna 10 bucks. Plug it into the back of the radio and either hold it outside the car or lay it on the dash and see if the noise goes away.
It could also be alternator noise. Then You have to filter the power supplied to the radio (B+) 12 volts and the clock 12 volts.
I think the antenna trick shouold help You out.

My late brother in law, an auto repair person, told me the problem with the radio on my old truck was spark plug wires. The truck is not worth the price of a new set of spark plug wires so I never tested the theory.

THE ANSWER IS YES!
YOU GOT RIPPED OFF.
THE GUY IN THE STORE IS NOT TECHNICIAN,THEY JUST WANT TO SELL THEIR ITEM.
JUST CHANGE THE ANTENNA ,YOU CAN BUY IT ANYWHERE,EVEN WALMART.
BUT ANTENNA FOR CAR AUDIO NOT FOR THE HOME OR ELSE.
AND HOW COME THE AM RECEPTION IS GOOD BUT FM NOT?
OFCOURSE AM IS GOOD,Amplitude modulation (AM) is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent. For example, changes in the signal strength can be used to reflect the sounds to be reproduced by a speaker, or to specify the light intensity of television pixels. (Contrast this with frequency modulation, also commonly used for sound transmissions, in which the frequency is varied; and phase modulation, often used in remote controls, in which the phase is varied)
SO THEY HAVE MORE LONG FREQUENCY THAN FM

The antena is 100% built in to the rear window there are not external elements at all that are accessible to me. Can I suction cup something over the wires in the window?