Now consider a few months after this hypothetical fake-and-refutation, what if Biden actually does announce an emergency threat to America, and people end up waiting a few days (or weeks, or months) for the refutation to come.
The “no such thing as trust” is not coming from this innovation in particular but rather the confluence of two general trends: 1) heavy reliance on digital media and 2) ever-increasing ability to fake digital media.
Note that you don’t even need large, successful falsified media campaigns to create distrust. All you need is for people to know that the capability exists, and trust is immediately damaged. Even trivially-detectable falsifications can end up being difficult to sort through if there are a billion fake pieces of information crowding out a hundred real pieces of information. This is true even if all billion fakes are trivially detectable by a human (which they won’t be).