It all comes down to the specifics in the contract. You bet that it's possible that Disney could say, "We'll pay for DW, but only if . . ." Of course, the BBC would have to agree to it.
However, I'm not worried that's the case. If Disney had more control, RTD wouldn't be the showrunner. No way is he accepting a reduced amount of control. Indeed, I suspect that a crucial condition for him to return was that he'd have more control. Given how much the BBC wanted him to return, he had the leverage to get those concessions from the BBC (the IP owner).