I think phrasing the relationship purely in contractual terms is misguided. For example, it's relatively clear that LeBron's short-term desires were pretty fundamental in shaping the Cavaliers' roster over the last few seasons all in an effort to keep him happy and his team competitive. Those short-term moves ended up harming Cleveland in the medium-to-long term. To be clear, giving Lebron that kind of control wasn't contractually mandated, but Gilbert did it anyway.
Similarly Lebron behaved extremely cavalierly (if you'll pardon the pun) with an organization that had gone out of its way and beyond its contractual duties to keep him happy. It's frankly not unreasonable to feel as if you've been slighted when you go beyond the terms of your contractual relationship and the party that benefitted from your extra efforts feels no need to perform anything beyond the confines of his narrow legal duties. What you saw from Gilbert was, in part, an emotional reaction to the unequal nature with which the parties dealt with one another. Furthermore there does appear to be some evidence that Lebron has known he was probably going to leave for years. If he knew that and allowed Cleveland to go to the ends of the earth on his behalf in order to keep him, then he frankly wasn't being straight with the organization. Add in the one-hour special and you've got a situation where one person really ****ed the other.
So yes, Jesse Jackson's entire framing of the issue has it wrong entirely.