I don't think it is such an irrational statement. A Gibson TB (GTB) sounds nicer, cleaner, more sphisticated, musical and less abrasive than an Epi TB (ETB), but it doesn't sound fatter. If anything it sounds leaner, because the ETB's mids are kind of all over, cluttering things up while treble and especially presence are subdued compared to the GTB. Deep bass I don't think there is much difference between the two. Way seems to like that grinding tone of an ETB just as he prefers a 4x12" Marshall cab set up to an 8x10" Ampeg fridge - he says he "can't hear himself well" with the latter. I find that 4x12" sound a little grating and prefer the fridge sound.
Way also plays Ibanez Icemans (both old and new) a lot and these kind of fall between a GTB and an ETB soundwise.
Generally, a GTB will always be heard in the mix (unless drowned out by incesssant double kick drum playing), but it will not dominate or cut through like a P or a Ric, even Entwistle wasn't as upfront when he played pure, unmodified GTBs. That is actually a musical quality I like with a GTB, because you can play it a little louder than other basses and still not step on other people's frequency toes. But some people prefer to grind. An ETB sounds a little akin to a Grabber (with more bass though) and Way was a P Bass player for many years before he switched to the TBird. I think the visual aspect of that bass (especially in tandem with Schenker's trademark Flying V) appealed to him more than the sheer sound. His bass sound - whether on record or live - is largely unremarkable irrespective of what bass he plays. He built his reputation on his stage moves (and dress sense), not by what he plays. Even the more devout UFO fans here will find it hard to hum one of his bass runs from memory (well, "Cherry" maybe excepted where he chords a little on the D and G string).
Incidentally with a GTB which sounds a lot clearer and brighter on this than any ETB I've heard would:
Wiki might be right here.
Uwe