Eureka! I wasn't sure what you meant at first, but started looking around and discovered what to do. For anyone, like myself, who might have fumbled over this crucial step in one of the tutorials, you need to open your Event Settings node (the very first one) and, for myself anyway, the solution was to scroll down to where it says Event Actors (add actor zero if it isn't there I suppose) and change 'Type' to Player rather than Object.
I also have, under 'Name Settings', the 'Use Scene Object' box checked, though I can't recall whether I checked this intuitively myself or whether it's automatic, nor can I say whether it's necessary-it's just the only other additional thing that's checked. Nor can I say at this point what the features, 'Use Root' box, the 'Child Object' empty field, or 'Set Name' box might be used for, but perhaps our friend GIL-the handy acronym who apparently runs this show-might decide to respond once more and better explain. For my purposes, this issue is effectively solved, and I'm grateful for the help. Cheers.