Does "any ~ ever ~" become negative?

Question

On Friday, Senator Richard J. Durbin, Democrat of Illinois, affirmed that Mr. Trump did use the term “shithole” during a White House meeting on immigration with lawmakers. Mr. Durbin rightfully described Mr. Trump’s words as “hate-filled, vile and racist,” and added,

“I cannot believe that in the history of the White House in that Oval Office, any president has ever spoken the words that I personally heard our president speak yesterday.”

From the context, it seems like the quoted sentence means "no president has ever spoken what Trump has said" or "Not a single one had said that til date except Trump."

So, my question is,

Does "Any + subject + has ever + verb" become to mean "no subject has ever done(verb) something"?

Answer 1

Not exactly.

The important parts of the sentence are:

I cannot believe + any + subject + has ever + action

They are not saying that no President has ever said those words.

They are saying they can't believe any other President said those words.

Essentially they are saying:

While I have not thoroughly checked all the words of every previous President, I don't think any of them has said the words that Trump did yesterday.

This is almost the same, but gives themselves a get-out clause, just in case a previous President did say those words.

Answer 2

What makes it negative is not the "any ... ever", but the "I cannot believe".

If I said, "I believe that anyone might say that", I am saying that someone might indeed say that.

But if I said, "I don't believe that anyone would say that", I am saying that someone would NOT say that.

The example sentence you give is more complex, but the idea is the same.

(I presume we're not debating the politics here but the grammar, so I won't get into the content of the statement at all.)