I highly disagree with the JB being bright. I don't get it, TBH.
I completly agree with Mincer about bright meaning different things for everyone, though. But I'm just speaking from my own perception/experience.
But any of Duncan's vintage-style windings are way brighter than the JB for me. Not to say they're bad or that I dislike them, but I actually find the JB somewhat dark by comparison.
I also don't find the JB thin. Yes, the low-end is not deep, but I've always somewhat struggled controlling the JB's lower mids. They can be kinda stuffy at times. I guess that's what people interpret as it being loose. But I don't personally find it loose (I personally find the Custom family way more boomy). Just kinda stuffy at times with some amps and some boosts like a TS808. Easily remedied, though, by going for a tighter boost like an SD-1.
Everyone has their experience and their perception. But I actually find the JB to be way darker and fatter than what many people give it credit for. I know there's been some statements being made about the JB being sort of a Tele-ish sounding humbucker. I personally find that statement ridiculous.
JMO, of course.