Why do people continue making references to whether or not an airline is in SkyTeam? You should find it probative that the DL language (quoted in the first post) mentions nothing at all about SkyTeam. That is because the dispositive inquiry is not whether the segments are on a particular carrier, but rather whether they are all on the same ticket. Indeed, it is rare to have a DL ticket involving non-SkyTeam members, but tickets involving AS are one such example. If I fly DL from JFK-SEA and AS from SEA-LAX on the same ticket, my bags get checked through, despite AS not being in SkyTeam.
It's annoying, but it's not complicated...