My source is the IBC section 803 (1), which I only know about because I've had the misfortune of needing to know about getting building permits for acoustically treating an office space in my career (which itself is a long and boring story about a failed startup).
The way the building code is written doesn't explicitly ban any material from walls/ceilings, but rather sets the constraints on the performance of the material when exposed to heat. There are higher limits for walls/ceilings than for floors because flames climb. Wall coverings (including wall paper and its glue) have to be flame retardant to meet code. There have been some infamous fires in the past, which is why this code exists (building codes are written in blood, as they say).
Most carpet doesn't go on walls, so it doesn't meet code, unlike wallpaper. And building inspectors are conservative people that are unlikely to permit you to do anything weird, even if you can prove by the letter of the IBC that some material is up to snuff.
