"The attack can't use external input e.g. clock because the NSA can't correlate generating the random number with seeing it in flight."

It could potentially use the number of milliseconds since the last hour, or maybe the state of the branch predictor, or any number of other things that have exploitable biases (with NSA resources, 1/1000000000 is pretty good odds).

Why should the CPU not have an internal counter that is backed up in flash memory between reboots? 128bit would be enough, with the highest bits set to the processor serial number. Using this counter in AES-CTR mode – i.e. encrypt the counter with the secret key to generate the pseudo random data – the NSA could reconstruct the internal CPU state from a single block (16 bytes) of random data. As many random data is published verbatim, for example as nonces, getting such a block should not be a problem.