How could household vinegar create a salt on car carpet?
I once had a humidifier and I ran it with tap water.  I soon noticed a build up of white dust on the carpet right in front of the humidifier.  I suspect your situation might be related to what caused my white dust.  Tap water contains salts (just like table salt), the harder the water the more salts it contains.  They are present in low concentration so you don't normally see them.  In my case, as more and more tap water evaporated it led to a visible build up of these salts.  In your case, as the water on the carpet dried, it left behind the same salts.  Maybe you really soaked your carpet with a lot of water, maybe your water is very hard, and finally, maybe salts were actually put into the carpet during their manufacturing process - and maybe washing them with vinegar (dilute acetic acid) solubilized the salts and brought them to the surface, making them visible upon drying.