Further, if it werent for his intelligent investing, he would have lost nearly all of the proceeds from that sale, like so many others did(1). It was exactly his smart investing that allowed him to _keep_ his "lucky" windfall
(1) http://investmentxyz.blogspot.com/2006/05/cubans-collar-anat...
With regard to the moves he made after the ridiculous Broadcast.com sale, all he did was lock in his profits. That turned out to be the correct move, but that doesn't necessarily say anything about his investing skills. It just shows that he realized that he had hit the lottery and wanted to insure his win.
Warren Buffett made his money through smart investing. Mark Cuban did not, so I'd rather listen to Warren Buffett and others like him than an opinionated guy that got lucky.
Public companies have a responsibility to their (rational) shareholders to minimize expenses that have no possible ROI. Taxes are chief among those.
If you're asking for my opinion, in my opinion what he is saying is absolute nonsense. The populist drivel spewed in those tweets is an attempt to appeal to his Shark Tank audience. If he appears relatable, the show's ratings rise and he gets the accompanying ego boost. He's doing it for the same reason that centimillionaire Hollywood types advocate for socialist candidates & ideals that are in direct conflict with their own financial interests: popularity.
Any company that has options available to it that will lower their tax bill without negatively affecting their income and growth prospects should pursue them. In fact, they have a legal responsibility to their shareholders to do so.