as far as I know, there is no scientific evidence or real testing that has been done to definitively say one way or the other.

It's been done by practically every reputable guitar manufacturer on the planet. (I know this because I was involved in some of them.) They just don't publish their results in scientific journals; they make their results known through sales literature, such as described in OP's post. I think this is a big part of why so many people take these claims as marketing BS rather than measurable data.

Different woods have different structural properties. Every species (and every tree (and even different branches from the same tree)) has slightly different resonant and dampening properties, which affects the way the wood reacts to and interacts with the vibrations of the guitar strings, and therefore the character of the sounds produced by the instrument (its "tone"). Is it a huge audible difference? Sometimes, but not always.

id be super impressed if anyone could actually say "oh, thats a mahogany guitar im hearing right now", but who knows...maybe some people can.

I assembled a bass at work one day, then called up the stairs to my manager and said, "Hey Sheldon, tell me what bass I'm playing." Then I played him a funky bass riff, and he shouted down, "(model of bass) with swamp ash body, maple fingerboard, and nickel strings." He was correct on all four details.

When you listen to a bunch of instruments every day that are identical in every respect (including being played through the same amp with the same EQ settings) except for the woods that they are made from, you start to notice trends in what the different materials sound like. Again, it's not always a huge difference, but it's a difference.