Pacific Daylight Time
I am now at our friend's house, using his WiFi network, and I find that I was mistaken.
When I was here last, I wasn't trying to use the Gmail SMTP server, I was trying to use the authenticated Verizon Wireless server (smtp.vzwmail.net), which uses port 25. The Gmail SMTP server does work with this ISP, but the Verizon server does not.
I can telnet to the Gmail server, but not to the Verizon server.