You need at least 7 contacts that use Secret, but approximately half (or 1/3 or 1/4, whatever gives the best experience) of your messages will come from people NOT on your contact list. That is, most of the posts will be from people you don't know. But enough will be from your contacts to keep it personal...
What they could do instead is only share secrets if you have N contacts in common. This solves the bot problem - the target will not add the bots.
You could also have some sort of threshold before showing secrets as well.
That said, I've never used Secret so this may or may not work. It'd be interesting to play with the Secret data to see how the social circles overlap and what kind of traffic patterns they see.
So that would kind of defeat the purpose of the "friends" stream entirely.