Thank you, Ebroadabroad, CPRich, Mwenenzi,mvoight, and Dave Noble, for your replies.
I did see that excerpt from the website, which certainly did seem to say you had to enroll first or at least simultaneously. On the other hand, when I enrolled everyone in American yesterday by phone it was for the express purpose of getting credit for the Jan 3 flight, and American didn't even hesitate at all at that, so later, I started to wonder, if maybe, just maybe, I could squeeze in LAN too.
As to my general comment about the hassles of creating frequent flyer accounts for the other four members of my family, I didn't mean to imply that it was necessarily more work than four random people, just that they do not accommodate families at all. With just a bit of effort they could at least make families a sub account so that it is easier to manage and I don't spend my afternoon playing data entry clerk (I'm not even talking about pooling benefits, just don't make me type in my address 5 times, please). Also, for example, I never made my kids JetBlue members because they each needed a unique email address iirc, and they didn't have one. And one airline ... Was it Delta? ... Wanted me to fill out paper forms and mail them in.
Heretofore most of our leisure travel was in miles so there was nothing for them to earn, but sometimes that won't be the case or sometimes I will just use miles to upgrade, so it's time to enroll them and it's just a pain.