Eden's press conference did nothing other than completely disrupt many of the Morgan's plans, forcing them to spend several hours which were spent on meetings, trying to come up with new strategies to make sure they were able to achieve the desired outcome.
They didn't have an option of backing down, since that would mean two things that they couldn't swallow no matter what.
First, their pride would be hurt greatly if they were to lose to a country which they considered primitive, especially after having several government institutions acting as their helpers.