I think the bouzouki player you spoke with understood that you might like to try his instrument; you were probably wise not asking.I actually like to have other people play my guitar/s. I love the sound of them, and am pleased to share the joy of these instruments. BUT ... I do understand people's reluctance, and I respect it.
I have actually had someone ask to play my harmonica's once, at a jam session. I refused. I can't imagine why anyone would want to be that close to all my mouth blowings! It seemed a little like swapping underwear.