There are many backup clocks/clusters that NIST uses as redundancies all around Boulder too, no need to even go up to Fort Collins. As in, NIST has fiber to a few at CU and a few commercial companies, last I checked. They're used in cases just like this one.
Fun facts about The clock:
You can't put anything in the room or take anything out. That's how sensitive the clock is.
The room is just filled with asbestos.
The actual port for the actual clock, the little metal thingy that is going buzz, buzz, buzz with voltage every second on the dot? Yeah, that little port isn't actually hooked up to anything, as again, it's so sensitive (impedance matching). So they use the other ports on the card for actual data transfer to the rest of the world. They do the adjustments so it's all fine in the end. But you have to define something as the second, and that little unused port is it.
You can take a few pictures in the cramped little room, but you can't linger, as again, just your extra mass and gravity affects things fairly quickly.
If there are more questions about time and timekeeping in general, go ahead and ask, though I'll probably get back to them a bit later today.