The errors you see in your mobile phone's positioning are due to signal problems (reflections, etc) and the relatively limited capabilities of the cheap GPS radio in your phone. A decent GPS receiver with a well-positioned antenna will get a highly accurate clock.
Speed of light is 299,792,458 m/s. So if GPS is off by more than 1/10,000,000 you can't get accurate within 30 meters. Having used a GPS they are better than that, thus the clock must also be at least that accurate. Of note, stationary stations can get into centimeter precision which imply's vastly higher accuracy.
Particularly if you're using it to sync between two different time zones that could well be looking at different satellites.
However, I don't know how much inaccuracy is introduced and whether it would have too much of an effect for the purposes of Google, et al.