As previously stated, the cuts made to the film are not a problem - in fact, the shorter version will probably be seen by most of the world, outside of the Asian territories where it has already been released - but the Weinsteins' title (Master of the Crimson Armor) was, as was their general approach to distribution of the film. Firstly, Kaige and others involved in making the film were concerned that the new title "emphasized the movie's male-oriented martial arts aspects at the expense of its other qualities," including lots and lots of romance. Secondly, Kaige and Stroh felt that their film deserved a wide release, much like the one granted Hero, which Miramax opened in over 2000 theaters nationwide in 2004. The Weinsteins, on the other hand, favored a more limited release.
In the end, they were unable to come to an agreement, and the parting seems to have been amicable. As long as the film finds some sort of distribution here, it probably doesn't matter too much who is in charge - realistically, a wide release is probably going to be a reach, no matter who ends up with the rights.