I think I understand how and why we see Tucker doing an interview with Frank Underwood.
If I was hired to produce that segment, here is how I would do it.
First, train the AI on the entire series of House of Cards to get an accurate reproduction of Underwood's voice.
Write the script for the interview.
Have the AI read the script in Underwood's voice and check carefully for errors. It must be very convincing.
Set up the set for the interview. Carefully work out how Tucker can direct his comments to where Spacey's head will be. Some colored tape on the wall would work to give Tucker a target to talk to.
Record the interview as though Spacey was there, while running the recording of the AI reading the script. Perhaps use earbuds on Tucker so the fake voice doesn't leak into microphones.
With Tucker's part done, turn the project over to the special effects crew to make a convincing Underwood speaking his lines in perfect synchronization to the fake recording. Add gestures and facial expressions to match Underwood's style.
Trust me, with 3D modeling programs like Daz you would even have a slider to adjust exactly how much stubble would appear on Underwood's face.
Then, sit back and note how long before the public figures out the trick, even after explaining it beforehand as a trick to watch out for. Watch the MSM run with the "Spacey for Prez" sensationalism.
This also provides a clue why they'd use a known set of episodes to train the AI voice in Underwood's character. Spacey can't sue because it's the voice of a character, not the real Spacey. They are not impersonating the real Spacey, just his famous character.
Do you think I'm close to the answer? Tucker would consider this worth risking his reputation of association. It explains everything.
Didn't look real to me. Also they show the back of tuckers head that camera angle is never in a live interview. Looked like it was to convince us they were in the same room.