I don't really think the original form is ambiguous in what it means, if you're familiar with the grammatical form used. When you have A and B, with C and D applied respectively, that means C is applied to A and D is applied to B. Word problems are about using both grammatical and mathematical skills, so the word choice may have been intentional. Thus, changing the wording to make it easier to parse would be missing the point. Or maybe it was just badly written.

The retelling done here and at many other sites change the question. Here it was turned into a dialog and statements were made that included information not present in the original. Consider "Then Cheryl whispered in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispered the day, and only the day" versus "Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively."

It is a logic problem, certainly, but in the original wording it was a grammar problem where I spent most of the time deconstructing the wording of the statements rather than solving the problem.

Yes, I saw the original question before I saw the rewording here. I still don't think it's that confusing. If anything, the original is less verbose.

though there were informations provided, I can render this question undefinitive, though the girl insisted on defintive answer (can I?)

and there is no tricky bullshit to do so...

I saw both the original and the Hungarian version. The Hungarian missed the "respectively" part, but people could solve the question even without knowing who the day and month was told, as I recall one extra elimination step was needed. I can't find the thread now and following other people's reasoning was even harder than understanding the question.

Anyhoo, it took me about 20 minutes to solve, in the first 15 minutes I didn't even knew how to approach the problem.