We're talking about different things here. In the linked article, Anna never accepts the invitation, nor does she propose alternatives. It's OK for someone to intiate contact more often than others, as long as the counterparty actually accepts the invitation every so often (or picks up the phone or chats or responds positively). That's not the case with Anna, who repeatedly says "nah" in the face of consistent kindness and consideration.
> as long as the counterparty actually accepts the invitation every so often
Per the article, the collegiate counterparty did accept other invitations:
We ended up hanging out quite a bit during those early months.
The social ritual in the article's title was specifically about party invitations:
“Why do you keep inviting Anna out when she’ll just say no?”
“I know she’s always going to say no, but that’s not the point. I invite her out so she’ll always feel included in the group.”
If it's indeed specifically about party invites and not other things, then you're right and I misread it. I wish the author were more explicit about that beyond just a fleeting line at the beginning "We ended up hanging out quite a bit during those early months."
My read was that Anna never acted like she's actually part the group because she's only ever shown repeatedly declining invitations.