Ricky, you're WRONG.
Obviously MU own the NBL license, doh. That is a license to enter a team in the NBL. Any 2nd Melbourne team will naturally require their own license. In the past, people have bought licenses and moved them to new teams and new cities. Not sure if there are any floating around for sale, or if they would simply apply to the NBL for a new one.
Doesn't really matter, either way any discussion of a 2nd Melbourne team PRESUMES that a license would be made available.
I've no doubt that MU "claims" the titles won by the Tigers and displays their flags, probably displays retired numbers too. Just as Brisbane will do, despite having no actual link to the previous team.
But simple fact is that the Trademarks for Melbourne Tigers are Owned by the Melbourne Tigers, NOT MU.
Whether or not that played a part in the re-branding, as has been suggested, I have no idea, but it is what it is.
PRESUMABLY when LK & Co tookover the NBL franchise, there was some agreement related to using the name, but it quite possibly had a time-limit on it.
Point remains though that the Tigers would be unlikely to secure enough backing to re-enter the league, and the brand would face the same narrow support hurdle it always did.