there are no problems with the file permissions

If you are getting a permission denied error I am afraid that there is a problem with permissions, however probably not an obvious one.

Can you add the following code between the if -e and the open FH2 line and tell us the results.

        my @file_stat = stat "$users{$user}/MY_FILE";
        my @dir_stat =  stat "$users{$user}";
        printf("%d $users{$user}         -> 0%o %d %d\n", $>, $dir_sta
+t[2] & 07777, $dir_stat[4], $dir_stat[5]);
        printf("%d $users{$user}/MY_FILE -> 0%o %d %d\n", $>, $file_st
+at[2] & 07777, $file_stat[4], $file_stat[5]);
[download]

Update: tidied up code no functionality changed.