I've confused you. I'm sorry.
The Constitution states: "In the advent of the death of the President, the Vice-President shall ACT [emphasis mine] as President." No title, no swearing in, no nothing.
So Congress WAS correct when they addressed John Tyler as Mr. ACTING President.
It was TYLER who insisted that he be sworn in as President and be addressed as "Mr. President."
Although this was probably NOT the intent of those who drafted the Constitution, this precedent STUCK--and has remained in place ever since, even though the wording of the Constituion on this issue has not changed.
"I say YOU'RE the CUTEST one. No, I say YOU'RE the CUTEST One. And we go on like that from dawn to three."