You asked if your boss could require you to do whatever, the answer is yes if you're an at-will employee. If you have a contract, his demands have to be in-line with the contract.
In White's case, traveling with the team is either a reasonable expectation or explicitly in the deal. He didn't show up day 1 because he wanted to be able to travel by bus and needed that language in his deal. Of course the Rockets were going to make some allowances for the guy, they wouldn't have drafted him otherwise. But they didn't want to give him exactly what he was asking for initially, or there would've been a deal before camp started.
If the Rockets said, "you either fly, or you don't play" and White's contract didn't say he doesn't have to fly, they would have been well within their rights. I'm sorry that reality doesn't align with your bleeding heart perspective.