We are told two things about the situation. You are assuming the first thing we are told can be trusted and the second can't.
I understand that the logic puzzle is only to verify the second thing we are told. I am not confused. The way that the puzzle is presented, though, allows for confusion, because we are presented with three things: 1) A physical setup which can be trusted (4 cards exist, we see 1 side of each card) 2) A statement that each card has one color and one number 3) Even -> blue on other side.
Given that one of the things we are expected to trust is a statement made to us and the thing we are expected to verify is a statement made to us, there is potential for confusion as to which statement(s) we are to verify. This potential is all that OP raised and all that I have been trying to explain.
Edit: To summarize in brief, as the problem is presented, it is not 100% clear that some statements told to you by the experimenter can/should be trusted.
The actual situation as given to us is not that there are 4 visible cars on a table. It is that there are 4 visible cars on a table that contain a number on one side and a color on the other side.
We are being told to verify the statement:
"Of the 4 cards placed on the table, which have a number on one side and a color on the other side, if the number is even then the other side must be blue."
If the color/number statement was left out of the original problem/video (it isn't) then your argument would be true, as it would be an assumption that is not listed and we would need to flip the 5 as well.
E:
And I suppose the blue card since it could have green on the other side.
"If Jenny has 5 apples and Bob has 5 apples and Jenny gives Bob 2 apples - how many apples does Jenny now have?"
We don't question if Jenny went and bought n more apples to give to Bob and might have 3 Apples or 5 Apples or 5+n where n is the number of apples purchased minus 2 because it isn't part of the problem and isn't part of what is being asked. Maybe she won an apple lottery and that is why she gave Bob 2 apples. Maybe she gave Bob 2 apples and later lost her other 3 apples in a fire.
If you begin by questioning the validity of the question - Jenny can have 0...n apples. Which doesn't do us any good for solving the problem.
"There are four cards. Each card has a number on one side and a color on the other side." These details are taken as facts as a basis for solving the problem.
If you are questioning if there is a color and number on the sides. Are there really 4 cards? What if there is a 5th card I'm not told about? What if we took 4...n cards and I found a card that invalidates the problem? It's ignoring the problem and coming up with a new one to solve.