Using your phone's GPS requires cooperation from your phone, however, triangulation by timing is not only possible, but even required by the GSM standard, the signal continuously measures and encodes your "latency" to the tower needed so that you'll start transmitting your block slightly earlier if you're farther away so as not to overlap with the time slot possibly allocated for some other device.

It's not as accurate as GPS, but it gives a solid estimate of your location that neither you nor your phone can prevent unless you totally disconnect.

There are several ways to implement E911-like service, and at least one of them doesn't require GPS. Your phone can usually be seen by multiple cell sites, so it's just a matter of accurate timing.