The cloths are the cheap, easy solution. The problem is that the do not dry deep enough into the groove. If you dry a record and quickly put it on the table and play it, you will see water pile up against the stylus. So, the bottom of the groove dries by evaporation leaving whatever was in the solution. Distilled water is not pure H2O, it is less contaminated H2O. Leave a puddle on a black surface and let it dry. You will see a white spot where the puddle was. That is what is left in your groove.
Blow drying is also bad because it is an evaporative method that leaves the same residue in the groove. Vacuum drying is handily the best if it is a good design. It removes the most fluid from deep in the groove. If it leaves a residue it is on the molecular level which may or may not be a good thing depending on what you are leaving behind.