meta knowledge - Explaining Cheryl's birthday

Relevant link : Cheryl's birthday

I understand the solution. But it feels wrong to me, because Albert cannot possibly make the third statement with the information he has at the moment he makes it.

Hear me right : if he does, and if it is true, then we know for sure the answer is what it is. But if I understand correctly, he can't.

The first statement eliminates May and June for everyone. Bernard, had he been told "14th", could still not deduce the correct date. But he was not told the 14th. So he can make the second statement.

Then, the only thing Albert can deduce is "Bernard has been told 15th, 16th or 17th"

These three dates are enough, with the first statement, to fully deduce the date.

Bernard is able to make the second statement because he as a piece of information Albert does not, and the second statement only provides little information to Albert.

I say again, if Albert actually makes the third statement just for the sake of the problem, and if the statement is true, I do understand why the solution is July 16th. But Albert, with the information he has after the second statement, cannot make the third statement.

Let's take an example : let the date be August 15.

Albert can still make the first statement. Bernard can still make the second statement, because "15" (initial information he has) and "not May/June" (which he can deduce from first statement) are enough to deduce August 15 at this point for him. Albert cannot make the third statement.

Now, the date is of very little importance. let the date be July 16th again. Albert can make the first statement. Bernard can still make the second statement, because "16" (initial information) and "not may/june" are enough for him to deduce the date. But the second statement only tells Albert "Bernard was not told 14th".

What would be a good answer to this question ? There are two possible good answer for my question. The first one would be "you're just supposed to accept the clues and not question them". The second would be a detailed explanation of why Albert can make the third statement righteously.

How can Albert, with the information he has after the second statement, make the third one?