Abuse mitigation may have been the (original) intent. However, it prevents sender verification because stanford.edu is not a designated sender for the external domains, and thus has no SPF records.
If I use SMTP to send via gmail with SSL/TLS over port 587, the headers show it hopping through 5 stanford.edu servers, and finally `spf=softfail (google.com: domain of transitioning xxx@gmail.com does not designate (a stanford IP) as permitted sender)`.
For this to work, either your mail client is not enforcing TLS be used, is not validating the certificates presented to it, or trusts Stanford's MITM certificate. Perhaps you should try port 465 with forced SSL.
If I use SMTP to send via gmail with SSL/TLS over port 587, the headers show it hopping through 5 stanford.edu servers, and finally `spf=softfail (google.com: domain of transitioning xxx@gmail.com does not designate (a stanford IP) as permitted sender)`.