> > The phones do not have actual GPS receivers
> > built-in: it's some funny business with cell tower signals, and they
> > call it "GPS".


Actually, it's called aGPS (assisted GPS) and uses time delay and
triangulation by the towers as well as satellite signals (which are
presumably relayed, with or without processing, from the phone to the
tower since GPS is a one-way down signal).
http://ezinearticles.com/?GPS-Cell-Phones&id=52208 


If I recall, the original question was how to use this to find a lost
dog.

According to http://www.travelbygps.com/articles/tracking.php 
Location-Based Services (LBS) providers have agreements with the
wireless network carriers to receive data from a cell phone and make it
accessible to you via an Internet web site or call center. Most all LBS
providers will be able to tell you the approximate last known location,
but beyond that, services offered will vary, depending on the type of
cell phone and the capabilities of the service provider. 

Sounds like it might work, until the dog decides to go for a swim, but I
assume the original poster wanted some kind of DIY solution rather then
buying another service.