The problem with cut up fruits is the knife they were using. I WOULD NEVER buy half a watermelon from a non jew store because what else was that knife used to cut? THey may have brought it from the back of the grocery where they have a little deli, they may wash it in the same sink etc.
NEver mind kashrus, but at least in a yiddisher store, we know/hope/expect that a yid has to wash with a tepel after making!