Yes, the question is what "part of it" the Red Sox would have had to pay. If another team paid half, the other half of about 6 mill would be on the Red Sox books for tax purposes.
What do you think, the Red Sox were keeping him in AAA to punish him or something?
It seems pretty obvious they calculated that promoting him was too much of a risk because of the tax hit. And they couldn't get any other teams interested in trading for him.