If the Batmobile on display is indeed an original prop used in either the 89 Batman or Batman Returns movies, then the paint certainly has faded over time, because the 89 Batmobile was matte black, and the Returns Batmobile was a glossy black.........
Considering how they store the props in the archive warehouse and seeing some other super heroes displays and especially the age of this bad boy wouldn't surprise me about the color fade, but to be honest the dark grey popped up in person, it wasn't black at all by any means.
Another caveat from seeing the bale, keaton, pattinson costumes is how monumental they are in person, damn, affleck was huge and taller than cavill!!!
I was shocked to see that keaton is close to 5'9, I always though he would be taller but damn I was over the moon seeing the original costumes and the dark knight bat suit as well.
the 89/92 batmobile was detailed though, this website couldn't let me post the *.dng format pictures because I took raw and hi res pictures for my own research purposes but that Warner Brothers studio was emotional to say the least, Worth it for the DC section alone.
The Batmobile shown off from the Dave_W video off the WB special one is the same from the display, with the dual antennas on top of the canopy vent and the wipers, Since the over head lights were on the showcase it wouldn't suprise if it gave it that greyish tone, under natural light it would be black like in the video!