I have heard of an incident with AA too. My nephew, dpesite my advice to the contrary, booked his LAX to DEL trip via ORD and ZRH. I had advised him against buying two separate tickets, LAX-ORD (AA) and ORD-ZRH DEL on LX, during the busy Christmas season. His LAX-ORD flight was late arriving in ORD, which made him miss his LX flight. LX told himt that they would try to accommodate him on a standby basis during the following days, but could not guarantee him a seat. He did get a hotel from AA in ORD for one night. He was stuick in ORD with no sign of being able to get out. We had to book him on AI so that he could get home.
Was your itinerary, by any chance two separate tickets? The danger about two separate tickets on different airlines is that if you miss the second airline's flight due to delay caused by the first airline, you are out of luck.

However, if the two tickets are bought in conjunction, you are protected. In conjuncted tickets, one airline validates the fare even if there are two separate non partner airlines. Often, conjuncting two tickets raises the farebasis.
I too have travelled o0n two separate tickets on two different airlines, but I am aware of the risks involved. It's very risky at busy times, such as the week before Christmas.