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And if one is left with only internal noise, why not simply use a nice clean source like a Zener diode?

Quite solidly agreed. Internal noise beats external noise, and there is no point in using a radio receiver when what you want is internal noise.

It may have been misleading to refer to a radio receiver chip: the noise generated by the chip will be entirely internal. It doesn't depend on any external signal "sneaking in"; the noise comes from the effective resistance of the first amplifier stage. Nothing is being "received", in some sense; it's just a big hunk 'o gain.

A Zener diode would be fine, but the design is a bit more complex, especially for wide bandwidths---you need to mess with biasing voltages, speedy op-amps, interface to CMOS, and all that jazz. You'd need external power (or a DC-DC converter). I wanted a super-simple design that people could just plonk down on a PC board. Two chips and some bypass capacitors.

Why not do both? A Zener is supposed to be a relatively high-level source of white noise, up to some upper bandwidth, so you could just feed the Zener voltage (through a blocking cap, if necessary) to the radio receiver input. See, you and the chip manufacturer are working at crossed purposes: a radio receiver chip is SUPPOSED to be a low-noise device. For your purposes, you WANT it to be a high-noise device, to minimize the significance of external noise. Since the radio receiver chip does some things you want (gain, maybe AGC), but doesn't necessarily add an adequate amount of noise, a zener would be an excellent addition.