Wrong user in activity when a non-author of a node edits the node.

This is by design. It makes sense in some case to show it like that. suppose admin only published the node, than we we sure want to see the normal actor displayed.

This can be easily changed ofcourse. Since you are using rules with tokens, you can easily choose the token of the currently logged in user (as uid and as !username). You have full customization.

The current setup sends out a false message when people collaborate in editing nodes. Thanks to Stalski's tip of customization, I'll look into that as a workaround for one community. For all future installations, I feel the default should be changed.

When User B updates a Node that User A has started, it would be correct to state either "User B has updated Node" (true) or "Node by User A was updated" (true, but less useful). It would be doubly incorrect to state "User A has updated Node" as it claims something happened when it didn't (User A did not update) and it does not tell something that did happen (User B did update).

What Stalski referred to, a case when the editor only publishes something and wants the original poster to be credited by Heartbeat, might work best as an exception. It seems likely that the general rule would be most useful and correct as "User B has updated Node". For the exception we could use either the term add or publish instead of update, as users don't perceive publishing a node for the first time to be an update: "User A's Node was published".

Tried customizing the settings for the rule "Log activity when published node is being updated" but didn't get it right with the provided help. What exactly should be put into the field UID instead of [node:author:uid] and into the field !username instead of [node:author:link] to display and link to the user who changed the nodes?

Here you have 3 possibilities the way I see it in the rules action administration.
I now used [node:author] (author being a entity with properties, thus accessible by [node:author:uid])

1. [node-unchanged:author] The author of the node before it was changed
2. [node:author] The author of the node, so if the author field is changed, this WILL be the new author
3. [site:current-user] The currently logged-in user, most of the type an admnistrator, nothing to do with the node->uid field.

Where the comment of daedalon is correct is that it is incorrect to state that userA did change the node, as it just might be the global logged in user (E.g. user1) who changed that node. In such a case, you don't want to see admin changed that node, even worse, maybe the node change should not be visible in the stream what so ever.

All things to think about.
What are your reasonings about that.

Generally, you should be able to use the tokens in the rules UI as you desire.
Default setting can be discussed a bit further.

Another example, I think daedalon suggests as well, is that the author is submitting a node, and admniistrators, cron tasks, whatever can come around and publish it. These are all dangerous ways of handling things.
In all those cases, I myself played with extra rules and playing with the conditions. Worst case scenario even split up heartbeat templates to keep things apart. E.g. when a article is published, it can't be the logged-in user, but for pages, it can be ... I dunno.

I am having the same need. The updater should display rather than original author.
This allows tracking who changes what.
Changing
User ID
to
[site:current-user:uid]

and

!username
to
[site:current-user]

seems to do the trick. However the username does not link to its user, only the updater and picture go right now.
UPDATE: I think this issue is raised to the missing piece, node revision author, in token.module:
http://drupal.org/node/252241

Well, as said before, I dunno what the best default is, but with configuration you can get it done.

However the username does not link to its user, only the updater and picture go right now.

Doesn't [site:current-user:name] or [site:current-user:link] doesn't work for you or am I missing something.

And also, I hope we are talking dev version for now, since much has been approved there, and fixed. A stable release should follow soon.
So I even ask myself if this issue couldn't be closed. I'll leave that answer to JGonzalez and Daedalon

In my opinion, this works by design. I did change the default for "heartbeat_edit_node" from node:author to site:current-user.