An airline generally only requires that a passenger present one passport at check in.
That said, when a passenger checks in, the passport they present is used to check the entry requirement of the destination country. If the passport does not automatically qualify for entry, other checks are done which may require other passports.
For example, if you book a flight from the USA to Australia, when you book the flight you are often asked for passport information. Let's say you are a dual citizen, USA and Australia. You might book the flight with your Australian passport, as this is the passport that qualifies you for the entry requirements into Australia. At the gate in the USA, you would present your Australian passport. On the return flight back to the USA, often the gate agent needs the passport that matches the id used to make the booking. However, you will also need to present proof that you are eligible to enter the USA. This might be a visa in your passport or a passport of the country that you are entering. When you get to customs, they will want to see the passport of the destination country, regardless of what the check in agent asked to see.
I have three passports and have gone through this exercise countless times between countries. How it was handled by the airline was inconsistent and there were cases where my checked baggage (firearm importation) and the laws of the destination country seemed to make a difference.
My point is that having multiple passports is not uncommon, so where the airline has to classify each person by citizenship, they may have to do some homework. The public expects a clear answer right away and are unforgiving of corrections, so it might be better to say "unverified" and buy some time than get it wrong and change the story later.
As an aside, when I file a passenger manifest for flying people internationally (privately) out of the US with EAPIS, there is only one identity for passenger citizenship, so you have to choose whether it is the origin or destination country passport if the passenger has both.