Many people have reported encounters with ghosts.

is this unacceptable by testimony?

We've discussed this before. Is testimony or "reported" incident verifiable? I saw snakes in my living room. I swear I saw them! Is that verifiable?

http://www.bing.com/search?q=reliability+of+testimony+as+verifiable&form=EDGNTC&qs=PF&cvid=f03f2d6ceafb4ac0952e279d1adaf4cc&pq=reliability+of+testimony+as+verifiable&cc=US&setlang=en-US