Alcohol rubbed on carpet using white paper towels (no colors) has removed rust stains, coffee stains, and pet stains containing multi-colors from food. My husband dropped a glass of purple grape juice on a light gray carpet. I immediately blotted it up with white paper towels to remove liquid. I applied pressure to get up the rest, then I used alcohol and white paper towels. It completely disappeared!
Source: I saw a carpet cleaner remove rust stains from a light grey carpet using this method