> GPS receivers will benefit from onboard clocks. This is perhaps surprising, given that the GPS signal itself carries time information, but it happens because the signal from the satellite is weak—comparable to the power of a lightbulb transmitted across a continent. Landscape features, buildings, and interference make it harder to detect. To track this weak signal, the receiver must precisely lock onto the broadcast frequency. The more stable the local frequency reference, the faster and more reliable this tracking can be.
> In hostile environments, such as battlefields, this becomes even more important. The GPS signal is vulnerable to jamming, and effective (but illegal) jammers are widely available and likely to be encountered in future wars. With precise timing information, GPS receivers could isolate the true signal above the noise of the jammer. The receivers could even allow navigation to survive partial destruction of the satellite network.
> Present-day receivers must determine their positions by using signals from four or more satellites simultaneously, but a sufficiently accurate clock could instead use successive signals from a single satellite. Other defense applications include frequency-hopping communication, bistatic radar (in which an attacker stealthily acquires a radar signal from a target illuminated by a distant transmitter), and sensitive monitoring of enemy communications. For these reasons, portable clocks are of great interest to militaries in several countries.
But yes, the receiver does have to measure small time differences between received signals; but that just requires a local clock with high resolution, not one with low drift or low absolute error.
For example, if your local clock is a second off, but still measures time intervals to pretty high precision (say, 0.01% - losing a second every three years) that's probably not going to mess up your location fix very much. Especially when the problem is overconstrained as it usually is intentionally. Compare the theoretical minimum requirement of three visible satellites to make a measurement with the 4-12 satellites that the system guarantees will be in sight at any time.
Receiver receives time “noon” from GPS satellite 1 at receiver-local time T=0.
Receiver receives time “noon” from GPS satellite 2 at receiver-local time T=2 nanoseconds.
Receiver receives a couple more “noon”s from other satellites, then uses its receiver-local time differences to trilateral its location.