Which freq did you hear this on? Most centers have access to a couple UHF discrete frequencies that are specifically allocated for high altitude use (above FL600). They're called "special use frequencies" and they're published in FAA Order JO 7210.3X (so I guess they aren't that secret). While
hook_dupin is correct that Class E starts above FL600 and the pilot may cancel if they wish, most U-2 pilots will at least remain under flight following and advise the center of any altitude changes. "Oxcart" is clearly an homage to the Lockheed A-12 (single-pilot predecessor to the SR-71 Blackbird), although I suspect you heard a U-2. The 9th Air Reconnaissance Wing out of Beale AFB in northern CA is the sole operator of the U-2 (well other then the airframes belonging to NASA) and they normally use the callsign "Piñon", which is a type of pine tree.
Top Gear's James May got to ride along in Piñon 93 in this video: