cns_make_post($topic_id, $is_starter ? do_lang('INSTANT_MESSAGING_CONVO') : '', $message, 0, $is_starter, 1, 0, null, null, null, get_member(), null, null, null, false, true, null, false, '', 0, null, false, true);

Found in sources/chat.php line 957.

POSSIBLE Fix (untested):
cns_make_post($topic_id, $is_starter ? do_lang('INSTANT_MESSAGING_CONVO') : '', $message, 0, $is_starter, 1, 0, null, null, null, get_member(), $members[0] === get_member() ? $members[1] : $members[0], null, null, false, true, null, false, '', 0, null, false, true);

What this does is set an intended_solely_for value to the ID of the user the message is being sent to, which is not counted towards post points when set.

___

EDIT: I was wrong. This does NOT work.

Better fix, though not entirely practical:

in the cns_force_update_member_post_count function of sources/cns_posts_action.php, find:

$map = array('p_poster' => $member_id, 'p_cache_forum_id' => null);
if (addon_installed('unvalidated')) {
$map['p_validated'] = 1;
}
$member_post_count += $GLOBALS['FORUM_DB']->query_select_value('f_posts', 'COUNT(*)', $map);

Comment out:
$member_post_count += $GLOBALS['FORUM_DB']->query_select_value('f_posts', 'COUNT(*)', $map);

This will cause caching to not count private topic posts towards a member's post count. That's the unfortunate consequence of this fudge, but at least it stops counting private topic posts towards points, especially when it comes to chat archive posts.

I noticed wherever in the Composr code exists a cns_force_update_member_post_count call with the second parameter specified ($member_post_count_dif), it is always within the condition that a forum ID exists. So it looks like the intention was not for private topic posts to count. However, cache counts them.

I could be wrong though.

I tracked the code, and tested carefully, and I think the base assumption is wrong - I can't see the problem occurring.

I tested manually making a PT, doing an IM, and in both cases the post count remained the same. The point calculation was correct. I cleared the topic cache and same result.

As your final post pointed out, the post count is only calculated for non-private topics.

Ok, I stand corrected - I reproduced incorrectly. It was related to the cache rebuild process only though.