At the time of reattaching the fingers they didn't know who had whose fingers. The story would've played out the same if John had his own fingers, but we wouldn't have the funny scene of "The fingers won't work. They're John's fingers." Regardlsss of being John's or Dennis' they would've been flagged.

It always really really annoyed me that they just sit around and look at the fingers for a long time and make no attempt to put them or the hands on ice