Note: What follows below is just a "core dump", don't expect 100% coherence or sense in it.
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Sometimes we do get uncomfortable when common friends are only able to talk about certain personal things with the other party (with whom are of opposite genders) rather than with us. And in serving our fellow brothers and sisters, we do find ourselves in such situations more frequently.

There are some inherent dangers with this. One is that of adultery (just talking from an assumed point of married couples). Though perfectly healthy and upright relationships can and do happen, as people living in a fallen world it is also equally possible for things to go overly close.

One plausible solution to that is for the open sharing to be done whenever there has been such a session, in order to keep the party accountable, and to support that party in keeping unhealthy practices in check.

Another is for guidelines to be drawn up as to how we'd interact with people of the opposite gender, so as to avoid overstepping each other's comfort threshold in the first place. I'd guess that as the relationship between a couple grows and changes, this would be one of the things that needs to be revisited and revised along the way, simply because the guidelines would vary based on the contexts, and the relationship at that point of time.

But what if there was a history? And one that might have been messy even? The same thing applies: we do what's best for the other party in love.

Finally, it would be important for all not to take this as the indicator of how good a person is, that the partner is able to show love in this way to the person that others cannot. This not only breeds jealousy, but also is the wrong way of looking at maturity anyway. And it is really unloving towards both the partner and the other person.