One of the problems at a DIY wash bay is the soap itself that may have been used OR the water. If the water source has a lot of mineral deposits in it, like calcium OR if the wash place uses recycled water (Yes it happens in areas that may have water restrictions that rinse water is recycled by filtering it to remove the dirt particles, BUT the minerals dissolved & suspended in the water are much more difficult to remove without special equipment and processing, something most wash places simply cannot afford to do), it may be that when the water evaporates. that mineral residue is left behind. The soap part may be a very high alkaline soap used to clean extremely dirty vehicles that may leave its residue behind.
I am guessing.
Did you try using a chrome cleaner on a test spot to see if that cleaned up the residue??
One suggestion if it is mineral deposits is to take a water spot remover to a test spot and see if that removed the milky residue/film. The Redneck version of this is to take some white vinegar and WARM water mixed at One (1) part vinegar to three (3) parts water and wash a test area so see if that removed the residue.
I agree that discoloring chrome is pretty difficult to do, since chrome is a very hard material. That said, I`ve see grasshopper bug guts "burn" or etch chrome when left to sit on a chromed bumper for a while (like 2 or 3 weeks before cleaning it off) due to the acid-forming chemical reaction between the grasshopper splatter (gotta be their digestive juices) and humidity (water) in the air. It ain`t pretty and even heavy-duty chrome cleaner will not remove the etching that takes place.