"Hand towel" probably means paper towels or wipes of some kind. Generally, you don't flush those. Toilet paper is thin, and tears easily when it's wet, meaning it can basically shred itself as it goes through the pipe system and avoid clogs (unless you use a shit ton of TP). Wipes and paper towels are thicker, and while paper towels still shred easily when wet, wipes are *always* wet, and therefore don't shred easily when flushed. It's possible that, in the past, the flushing of wipes or paper towels resulted in a clog - similar to stores that put signs that say "do not bring merchandise into the restrooms" on bathroom entrances or "do not flush merchandise" in the stalls themselves.
