I also got this problem, on one computer only; I've got a laptop which does not display this behaviour, i.e.: when I double-click an m-file, it opens it in the editor when Matlab is already running, and starts Matlab when it isn't. And I've got a main pc, which does display this behaviour, i.e.: when I double-click an m-file, it opens a NEW instance of Matlab WITHOUT that file in the editor.
Changing the file associations, as mentioned here several times, doesn't do anything, since m-files are already associated with Matlab (it would open access if they were hijacked). Reinstalling Matlab does not solve the problem.
However, I did notice something odd; it opens a dos-window just before starting Matlab. Might that be the cause for the behaviour?