In main.cf, use:

smtpd_restriction_classes =
  has_our_domain_as_sender

has_our_domain_as_sender =
  check_sender_access hash:/etc/postfix/our_domain_as_sender
  reject

smtpd_recipient_restrictions =
  check_client_access hash:/etc/postfix/internal_networks
  #
  # If the Client is in the our networks 10.* or 192.168.*.* networks, we
  # return "has_our_domain_as_sender".
  # "has_our_domain_as_sender" is defined as
  # "check_sender_access hash:/etc/postfix/our_domain_as_sender"
  # which will only return OK if the sender is "example.com" or the 
  # empty sender (for bounces!!), otherwise reject.
  # 
  check_sender_access hash:/etc/postfix/not_our_domain_as_sender
  #
  # The client is not in 10.* or 192.168.*.* (otherwise
  # the previous restriction would have matched!).
  # Now we check the sender. If it's example.com NOW, then 
  # somebody from the outside is trying to use a example.com sender
  # Thus: 554 Bloody liar!
  #
  reject_unauth_destination
  # prevent relaying
  ... other spam checks ...
  permit

/etc/postfix/internal_networks:

10               has_our_domain_as_sender
192.168          has_our_domain_as_sender

/etc/postfix/our_domain_as_sender:

example.com       OK
<>               OK

/etc/postfix/not_our_domain_as_sender:

example.com       554 Bloody liar!