must first pass through the amp which is their preceding component so does it not stand to reason that in order to receive an accurate example of whatever is behind it, it must be honest?
It can be honest as Mother Theresa, but if all she has to pass on is the lie she's been told by the source your "accurate, honest" amp will not really start benefiting you until you feed it the truth.
I visualize like the childhood game of "Telephone" where there is initially a message written down on a piece of paper. The first kid in a line of kids is allowed to read the message on the paper, then they whisper it in the ear of the kid next to them. They in turn repeat exactly what they said to the next kid. And so on until the message gets to the end of the chain of kids. Most of the time there are 'weak links' and the message is quite distorted by the time it reaches the end. Sometimes it actually made in there verbatim. Your good amp is like having one "perfect" kid, right in the middle of the line, who hears and conveys the accurate message along 100% of the time (not very likely, but lets just imagine). Having a poor source would be as if the first kid in the chain were dyslexic (in which case you would never get an accurate accounting of the message on the other end).
Don't get me wrong, an honest amp, a clear conduit for the truth, is certainly money well spent. That just ain't the whole story, as I bet we can all agree. On the rest, we can all agree to disagree.