I think there is a difference between making it clear to a person they'll always have the option to join - and pushing that person to join.

Anna in the story did not express regret that she never joined. And as far as we know, Alexei wasn't expecting her to take his invitations either - because it wasn't about actually getting her to go to the party, it was just about communicating to her that the "we've stopped inviting you to our group events because you always say no" moment never happened and she was still a part of the group. That was what she had appreciated in the end.

On the other hand, what your group attempted seems more like a concerted push to change the person's behavior. Most people would probably reject that if they want to stay in control of their own plans.

What? The group's behavior is basically just being a group of friends and inviting another friend?