Anyone can post anything to a person's inbox. However, #snac does a lot of checks to see if this post deserves to be here, e.g., if you are explicitly mentioned, if it's from someone you follow, if it's a reply to a conversation between people you follow, if it contains a hashtag you follow, etc. There are many more conditions. If none matches, the message is dropped with a log message similar to "post xxxx not for us". On the other, whenever a post from someone you follow gets in, snac tries to retrieve (following the inReplyTo fields chain) all the conversation up to the beginning to give you some context in the conversation. It may happen that, if that account you follow deletes their post, the replied post is left in your timeline, for no apparent reason.