It boils down to this, should Fox go forward with merging with Time Warner they are going to have play nice and offer concessions. There is no way around it. Fox already signaled a willingness to part with CNN should they gain control of it, which is a move entirely meant to help placate the regulatory bodies.
Disney could very easily throw a wrench into the deal by filing challenges to it, effectively delaying it or derailing it entirely. They could allege a conflict of interest as Fox would be in direct control of the properties that are owned by Disney (i.e. Marvel), which is obvious. This would very much be a legitimate challenge that Fox would have to answer to.
Fox could easily overcome this by volunteering to relinquish the X-Men rights back to Disney/Marvel, demonstrating good faith in upholding direct competition. This is crucial because anytime two large competitors merge, the government's position is automatically to challenge the deal on grounds of decreased competition. Releasing a well known valuable property (X-Men) that is a direct competitor to a property they would be acquiring (DC) back to its original owner (Marvel), would effectively strengthen Fox's argument for approval of the deal and would ultimately help strengthen competition overall. The other end of it is that it makes no sense for Fox to hang onto the X-Men rights. Not when they stand to profit from everything they can with DC properties that they don't currently get from any of the Marvel properties, such as merchandising. Why promote a competitors property for them when you can promote your own and profit on multiple levels? This is exactly why Disney does not promote any of the properties under Fox's control, and in either case it makes total sense.
The whole deal with DC, and Marvel property film rights is just one piece of a much bigger story that would be taking place. To understand why Fox would be (potentially) effectively give up X-Men for practically nothing (on the surface anyway), you have to step back and analyze why they want to merge with Time Warner in the first place. Compared to the bigger picture, the film rights of X-Men would be a small sacrifice compared to gaining a prize like HBO for instance.
Ultimately the two do compliment one another. Fox is a major Broadcast TV presence and film studio. TW is a major cable TV presence and film studio. The two combined could potentially create valuation that would almost rival that of Disney, which is no small feat. The biggest threat to both of them are the content delivery businesses (Comcast, AT&T, Verizon, etc) which have been consolidating. Having enough clout for Fox and TW to counter those companies is why Fox wanted to hook up. TW resisted, but now it appears that a chorus of investors is slowly growing to push TW in that direction. If Fox changes up what they attempted with the original bid and provides voting shares instead of non-voting for example, this may accelerate this movement.
There is no way Disney would be able to acquire Time Warner on purely regulary gounds alone. Their scale is already huge, and increasing it further would start to move them into monopoly territory as their competition would be outright dwarfed. Now, buying up CNN specifically they could get away with as they do not have a presence in the 24hr cables news space. They have ABC News which is predominately broadcast news, but little in the way of cable news. Fox however, does already have both.
Right now it's just conjecture and speculation, but it is fascinating to think about what might come of this should it become a reality.