Yes, and we have artifacts (I believe they're called antiques :-)) from that time too that tells us what color clothes were, signs, etc. So we should be able to do alright.
eg, this blue:
24. Scotch Blue
Throat of Blue Titmouse.
Stamina of Single Purple Anemone.
Blue Copper Ore.
Maybe that's because those others are more likely to do a bad job, because they lack the training to do a good one. Sort of like how sci-fi filmmakers have taught millions of people that you can hear explosions in space and that lasers make a "zap" sound.
BTW, if you want to support some folks that actually try to get it right, check out the expanse.
Also, we still have the techniques and materials used to make old paints. New batches can be whipped up (assuming they aren't too toxic) for comparison. Lead based paints obviously are more problematic, but modern technology is really good at replicating paint colors.