Rabbi Of Berlin: I just looked it up: Osek bmitzvah does apply to milchemes mitzvah too. The Mishna discusses a machlokes if a war of defense constitutes a mitzvah or not with regard to the war being considered a mitzvah that would patur other mitzvos (Rambam) and in any case the Halacha clearly is against Rabbi Yehuda, i.e. a war of defense is not considered a mitzvah with regard to this.
So the original statement is true: Osek b’mitzvah patur min hamitzvah.