That's a little out of context, Trop. The resistance to Mesic assuming the chairmanship of the presidency was based on the fact that Mesic was by then a member of the HDZ, and HDZ's official platform, which, Mesic reiterated, was the dissolution of Yugoslavia, and to be its "last president."
The military had no choice: sworn to uphold the Constitution and defend the country's integrity (physical) from enemies, foreign and dmoestic, could not have possibly supported such a man. Besides, the Presidency, not one member, had the power of a collective commander in chief, so to say that the Army refused to obey Mesic is taking it out of context.
Dissolution of Yuglslavia could have ben accomplished legally only by acclamation. Yugoslav Constitution required concensual agreements in order to avoid outvoting by simple majority (mayorizatsiya).
The fact that Miloshevich did secure 4 votes out of 8 placed Serbia in a better position with respect to the rest of the lobsided federation, but certainly not in the leading position. After all, 4 was only 50%, and concensus was required.