It doesn't seem like a bad thing that they do care. The end result in the study was that people trusted the person who doesn't make time for them less. But that's exactly the right result. You should be less close and show less trust toward someone who won't make time for you, since they are, by definition, not going to be there for you as often when you need it. It seems quite natural to move trust and closeness to a party that, for whatever reason, isn't going to decline invitations to engage. Nothing wrong with the other party if they have other priorities, but it does mean they aren't a good person for the inviter to depend on. Sort of avoiding codependency.