The path of the vector of attach changes but it doesn't go away. Corp B could just bribe an overworked and underpaid mail room worker at Corp A to make some copies of sensitive looking info before they deliver it upstairs. Even today, who is to say that this doesn't happen with some overworked and underpaid sysadmins? or secretaries with their bosses email account password? I wouldn't be surprised if bribes for emails happen pretty frequently in the business world even today.
Email cam be copied and sent wherever without the operators knowledge, from anywhere with internet, if they break into the mail daemon.