In theory, the mount point permission do not matter. In several cases it _does_ in fact matter but I suspect that isn't what's causing your issue here (but just in case, my 'works for eveything' mount point permissions are 0555).
The filesystem mounted on top of this mount point has it's own permissions though which are probably where your problem is.
If the directory your file is sitting in does not grant you write permissions, you'll not be able to delete files from it (even if you own them) or create new ones. Write perms on a file only allows you to modify the contents of the file.
This applies to any dir, regardless of where it sits with respect to it's host volume.
Sing out if I've missed you point of course