What kind of false positives are you getting? If this is occurring, it's possible there is a misconfiguration somewhere that needs to be addressed.
Beyond that, you could make a policy based off the sender address being null(<>) and have some stricter spam rules. You would want to be careful with this so that this policy does not trigger on outbound mail. Hope this helps. Thanks.
Do you have an SPF and/or Sender ID record in DNS for your domain and, if so, are you using "~all" or "-all"? If you are able to use "-all" (for a hard fail of messages from senders not authorized to use your domain) that might help nip the problem in the bud--but only for receiving mail servers who utilize these features for message reputation.