Yes it does. mtimes can definitely be edited, if you have permission, but it is rare. I have a photo script that pulls the taken time from Exif and writes it to the file mtime.
It just requires you to be the owner of the file (https://serverfault.com/a/337810), no special permissions. On the other hand, editing the ctime is not easy -- it requires tricks (e.g. change the computer clock, which typically requires root privileges).