The Loop-In feature allows you to involve anybody in a discussion thread via email, without actually giving them access to your project or Basecamp account. The person you loop in gets an email notification with the full history of the discussion thread - and nothing else. If they reply, their response is added to the discussion thread, but they can't click through to open your project or your account.
If people need to be more involved in your projects, but you still want to keep things off limits, check out client projects.