It is not whether the page is right or wrong, since it is merely reflecting the mess this whole punctuation business has become.

I repeat: What is INSIDE the quotes is supposed to be a direct quote of Paul's words. His words end with a full stop:
Paul : "Give it to me or suffer the consequences."

So, when reporting his Direct Speech, I place a Full Stop at the end of his words.

"Give it to me", said Paul, "or suffer the consequences."

Let's make it more emphatic:
"Give it to me", said Paul, "or I'll kill you!."

Now, the page says: Exclamation marks and question marks according to logic.
Logic dictates that it is Paul who is being emphatic, so the exclamation mark goes inside the quotes. It is also logical that Paul's words end in a Full Stop. So a Full Stop goes inside the quotes, making one outside redundant.

Just one more observation: "this whole punctuation business has become" such a shamozzle, continue what we were both taught, and see the logic in it.