You may be right on these specifics (and I'm sure Twitter's lawyers will spend hundreds of hours searching through all the possible permutations), but on the other hand, as long as someone is acting in the capacity of a corporate officer with duly appointed authority, and makes an agreement in that capacity, then the agreement binds the corporate entities. Whether that officer then informed other members of the company may not really be material here.

Just ask yourself whether this would be a good general policy: corporations get to escape contracts if their exec promises something and then leaves, or they just 'conveniently' forgets to inform other execs. In that world, how can any two corporations agree on anything?

Note that if an exec really does enter in a huge future liability and fails to inform the corporation, the usual way it should be resolved is the corporation is still liable, and then the corporation sues the former exec for failure to execute duties properly, with the sudden unanticipated liabilities going towards proving damages.