So to map your files with user id 1001 in /mnt/wrong to /mnt/correct with user id 1234, run this command:
sudo bindfs --map=1001/1234 /mnt/wrong /mnt/correct
C. Danescu-Niculescu-Mizil, R. West, D. Jurafsky, J. Leskovec, and C. Potts. Proceedings of the 22nd international conference on World Wide Web, page 307--318. Republic and Canton of Geneva, Switzerland, International World Wide Web Conferences Steering Committee, (2013)