All they're saying is that with absolute synchronicity among all of the clocks at all of their co-located servers, all pieces of the order are executed at multiple exchanges at precisely the same time. Even very small differences among the clocks at each one can create opportunity for others to step in front of the trade, and this helps them avoid that. While this may sound obvious, they wouldn't be doing it if it hadn't been a problem for them in the past.
Nanosecond differences are too small to take advantage of, that's only 30cm. My guess is that you'd be at least in (or close to) the microsecond range before you'd worry about HFT stepping in front of your orders.
If you're hitting multiple exchanges, then you can take milliseconds and still be fine.
One of the things HFT firms take advantage of is increasing a nanosecond lead into a microsecond (or more) lead by route optimization. If they can get information from one exchange to another faster than the original order, they can effectively trade by looking into the future.
Many firms invest heavily in direct microwave links for paths normally served by fiber because of the speed advantage.
Speaking from ignorance here but 10s of milliseconds sounds way too high.
This Wikipedia article [1] shows the standard Chicago to NJ connection at 14.5ms roundtrip and the dark fiber line Michael Lewis talks about in Flash Boys at 13ms.
Microseconds are not enough, because the arbitrage works by the HFT setting the order in one place, and then rushing the arbitrage to the other place. As long as you're more coordinated than speed of light between the two locations, you're fine.
Also, GPS clocks are cheap and precise, atomic clocks seem gold plating. (Which sometimes is actually necessary in electronics, BTW...)
I think the main innovation in Spanner is the notion of Truetime not the atomic/gps clocks though. In fact MSR has come up with something called ClockSI that does global snapshots with a modified NTP I believe.
