For me, I simply prefer the looks of fretboard woods like maple and ebony. But the other day, I had the opportunity to A/B my black/maple single-humbucker Stingray to a black/rosewood single-humbucker Stingray with the same strings. My Stingray was built between 2006 and 2007; the one in the store was likely a 2008. I set the EQs flat, maxxed out the volume, I ran them into the same amp, and tested them both with my fingers and one pick.
The concept... comparing only the effects of the fretboard difference.
It was a bit of a surprise... mine (the maple-necked one) DOES sound brighter. I was going to cite the strings, but my strings were worn-in Slinkys, to the same spec as what comes on stock Stingrays.
Perhaps if I knew how old the strings were on the rosewood Stingray in the store, I could be confident in the results of my comparison. But it was literally the cleanest (and thus, the newest) looking Stingray in the shop... so it couldn't have been that old or played much at all. And I hadn't seen it the last time I went there, about two months ago.
Whatever the reason, there was a slightly noticeable difference, and while I'm not 100% certain that the fretboards were responsible for it, there's certainly some evidence in favor of citing them as the explanation.
But at the same time, it's a subtle thing. And an EQ adjustment could make up for the difference rather easily...