No, because the passport doesn't explain how old you were when you left that country.

My passport clearly shows I was born in the UK, but my parents brought me to use the USA when I was just a few years old, so to my (grown-up) knowledge I never had a UK passport, only a USA passport. (This was by ship circa 1960, and I have no clue what passport requirements if any there were for transoceanic ship travel back then.)

There are oodles of people who were born in one country but their parents brought them into a different country at a young age, and thus they don't have a passport for their birth country.

But the passport has no clues as to whether you're in that situation, or you immigrated recently.

So all the country of birth on a passport can provide is a pure guess. And I don't see how passport authorities can demand a different passport from you on a pure guess.

They would have to be able to search your name and birthdate information right then and there and determine that you had another passport to be able to prove that you have another one that you have to present. Now, perhaps some countries do have that type of "live search" available at every passport desk today, I dunno. But if so, I suspect it's a fairly new development.

Obviously, given what's been revealed in the news recently (about stolen passports), it would be good if all passport desks could do a live search on passports, for checks against Interpol lists of stolen passports, if not against whether you have another passport in another country. But if they're not yet checking so well for the former, I don't see why they would be checking that much for the latter.