When an activity update is posted, the function bp_activity_post_form_action in wp-content/plugins/buddypress/bp-activity/bp-activity-templatetags.php is called. This function sends defines:
BP_ACTIVITY_SLUG is just the url of the activity (http://example.com/activity). To this url I added /post, and I tried it in the browser. I got the extremely informative error: “Are you sure you want to do this?” Now, I guessed, it would work without the /post-ending … and it did. (I had deactivated a number of plugins, but now they are activated again).