Actually, you do have access to the atomic clocks. The clock itself is Stratum 0, so a Stratum 1 server is the time server for that clock - it translates the frequency pulse that the clock gives off into a timestamp that can be served over the network. Something has to take the pulses from the atomic clock and turn it into time that we can use. A Stratum 0 clock is a frequency generator. Having direct access to it wouldn't help you much. You can buy your own rubidium frequency source for ~$1,500 to $5,000 or your own cesium frequency source for ~$25,000. The ntp program can take the frequency from that, along with time information from other Stratum 1 servers, and turn that into your very own Stratum 1 server. But that will still be a Stratum 1 server.
Don't forget, the number of seconds in a year isn't constant (it isn't even a linear decay), but an atomic clock doesn't know anything about the rotation of the earth. So all the Stratum 1 servers have to talk to each other and agree what time it is. Occasionally leap seconds are introduced to account for variations in earth's rotation and orbit. If we just defined a year as a set number of seconds and let the clocks run independently of each other (they would in fact keep perfect time with each other), you'd eventually find that the time of day no longer really corresponds to a sun position in the sky.