Should a disagreement always be settled "privately"?

If a very High-D person (not one of your directs) in a meeting raises an issue that could be seen as a conflict, can it be always be addressed in the meeting, or can it be better to avoid the subject and talk to that person separately later?

In general, rules of conflict handling say that it is better done in a one-on-one than in public. My intuition would say, however, that a High-D raising an issue in a meeting in a very direct way would expect a direct response. Probably, they are trying to make an important point and would like it to be clarified. But I'm a bit worried how this works on the "innocent" bystanders, especially if they are High-S / High-C.

I have been in this kind of situation myself as R&D manager in industry, where a very high-D marketing manager would make his point in borderline acceptable bluntness (style "your proposal is b***t, because...") and I know that he appreciated my direct responses. In those meetings, most of the other attendees were relatively High-D department managers, who shudder but accept the result. Now I am in academics, and it often happens that other participants are much lower on the D scale. Now I wonder how such people would take the situation. May they become afraid to voice their input on any subsequent subjects? Can that risk be averted by another way of handling the situation?