I looked around but I don't see any way to make this not happen - when using the "All Activity" feature to see the latest posts etc., it bumps blogs to the top of the stream if the poster edits it. It's not the end of the world, but occasionally someone will edit their blog quite regularly, causing it to stay at the top of the queue for all users and it looks like new content when it's not.

Is there any way to make this not so?

I'm afraid, this is intended to happen when content is edited. If you do not wish for this to happen, I would advise creating a topic in our Feature Suggestion forum to change this.