For solid body guitars, that's probably true. Just be careful not to overgeneralize. The density and other characteristics of the wood have a huge impact on the sound of acoustic instruments.
I would say it also has an impact on a solid body guitar. Why are the very most guitars made of wood in the first place? Different material WILL sound different. Even a fatter neck will alter the sound.
Take an electric solid body guitar, leave it unplugged, strum it. Take a different one, strum it. They won't sound the same. Although the pickups only pick up the vibrations of the string, the whole material of the guitar has an influence to these vibrations.
I have a Japan Jackson with a very thin neck. Unplugged it sounds dead, and guess what, it also sounds dead when plugged in, so pickups can't change this.
But I don't say a pickup-change is a waste of time and money. And I'm Mr "if cheap (or noname) does it, don't go expensive (or brand)" anyway.
If the guitar sounds nice when unplugged but suboptimal when amplified, chances are that a PU change turns it into something good.
Hey - been there, done that. Twice. The Jackson was hotter afterwards but still lacked life (that's why I bought a replacement in the end)... but my Cheri Telecaster improved a lot by putting in some DiMarzios.
I also have an Epi Les Paul Custom by the way, and - I don't know why - I quite like its stock tone.
