I took a quick look at both mednafen and pcsx-reloaded. Both use slightly tweaked JFIF coefficients, not quite the same but not nearly the magnitude of difference we'd be looking for.
I decided to capture output from pcsx-reloaded and... it looks like the coefficients are not the problem. The colors in pcsx-reloaded are rather different than the ones in psxjin, and the pcsx-reloaded colors look much closer to the originals.
But, those coefficients are almost the same ones as psxjin uses! (And the miniscule difference between them is not big enough for this). So there must be some other mdec error causing incorrect colors, perhaps something in the IDCT?
Whatever it is, it's out of my league, and I doubt anyone else will be interested in fixing it. Meh.
Edit: Note that the slight decrease of redness going from FMV->backdrop (especially visable in the pcsx-reloaded capture at the top left corner) is also visible in my analog cap from a PS2. So I think pcsx-reloaded probably has it mostly or completely right.