Adiabatic heating at high speed can easily give those temperatures. The plane needs approx. Mach 11 or 12 to achieve orbit; at Mach 5, the compressor inlet would see about 1300 C air temperatures due to adiabatic heating (depending on local static temperature). To/Tstatic = 1 + (r-1)M^2/2
Without pre-cooling, there is no room left (at Mach 5) to add heat via combustion (and thus generate net thrust) before you start melting the walls of the combustor - and that is for a ramjet that has no turbine blades. For a turbine engine, even one that can bypass a large fraction of the air flow away from the turbines and operate in partial ramjet mode (i.e the SR-71 Blackbird), the upper limit is about Mach 3 to 3.5, and those speeds are at high altitudes where air is much cooler to start with.
Big problem, it would seem that an awful lot of LN2 needs to be carried to do all that pre-cooling...and an awful lot of structure for the tanks, pumps and heat exchangers. Not clear if there is a net weight savings due to carrying less oxidizer for the rocket stage, but presumably there is (or will be...on paper...). If the N2 boil-off was allowed to happen at a high enough pressure that it could be used for film cooling in the turbine and/or nozzle, then maybe there's a net advantage...or I might be missing some other trick to tweak a bit more thrust from venting the N2.