Even within Schengen, Airlines can demand passport or national identity.
Everyone, public carrier or Joe Public is held legally responsible for transporting an illegal immigrant across borders, and not just across an 'external border'.
I am Irish, and I have lived the best part of a dozen or more years across the EU and have read debates within various groups about having passport on hand for inspection. I don't have the URL now but I was pointed towards an EU legal document that said there is a legal requirement for the traveler to be able to prove residency.
The methods to prove need to satisfy immigration/law officer are not explicit. Thus even a Q&A with an officer could prove sufficient.
I know of this being tested in Prague, CZ where a few Taiwanese students were jostled by police for not having any ID on them. They called a contact at the Taiwanese embassy (who I was having dinner with) and it was sorted out over the phone. I have also been checked on a CZ/DE train without my passport. I was able to provide my UK based license, plus answer questions about my German home address which satisfied the officer (who politely reminded me to carry my passport or national ID next time to avoid problems).