Thank you everyone for your responses re Basic Economy and ITA. It makes sense that BE is not a separate cabin and thus not differentiated by ITA (except via booking code). An airline's own site will of course explain which fare is which. However, OTAs and partners won't.

This means that in complex itineraries involving multiple airlines, you could inadvertently find yourself in a flight without checked luggage or seat-selection privileges.

This happened to me on a JL segment in a complex itinerary involving AA, CX, MH, and JL. As a OneWorld Emerald, I received the normal elite treatment on the first three carriers, but JL wouldn't even let me choose a seat till very close to the flight date. Ironically this is something you can routinely do on various airlines where you don't even have a status. For example, I have no relationship with Air Asia, but during the same trip could choose decent seats on their flights for a small fee. At JL I was completely locked out. (It seems that the only way out is to research each segment's booking code and then call to up-fare while purchasing. What a pain.)