It is not your job to prove anything but perhaps redeem your nearsightedness and holier-than-though attitude to thousands of intelligent audiophiles like myself who not only DON'T 'buy-in' to unsubstantiated hype but who simply trust their ears to know what's true and what's not. If YOU can't hear differences then that simply means YOU can't hear differences...it doesn't mean that I can't nor many[ if not most] people who actually take the time to listen, can't. By declaring us a small minority who have been brainwashed by preachers when the sales of aftermarket cables is a multi-million dollar industry that includes scores of manufacturers who offer take-home trial periods with full money-back guarantees if you're not completely satisfied, is not only an incorrect statement but also a direct affront to and attack on our characters as being inept/gullible and foolish. Then you tell us that this in turn qualifies us to live in "Bizzaro Land"... all because we don't agree with almighty YOU... Your arrogance about being "Right" is so laughable you should be very careful not to fall off that extra high soapbox you seem so assuredly standing on. . Declaring that we are essentially morons because we don't agree with what YOU seem to think as logical and impossible to argue with essentially reduces YOU to a glob of glue...fitting and waiting for the full gamut of [justified] derogatory adjectives which would appropriately "stick to you" if I weren't such a gentleman and on a public site where such name calling is not only inappropriate but would effectively reduce me to the status you so obviously have no regard for wallowing in.
As per the original question: it is not necessary to use the power cord of the power conditioner, there's a good chance you will find several which could make an excellent improvement in your system's sound.
Power cables make a real difference. Anyone who would like to improve the quality of their systems should be open-minded enough to try a moderately priced one or two from one of the many available companies you can find right here on Audiogon. Ask about their satisfaction guarantee and return policy...and buy with confidence. Best regards.