Yes, the spec is a bit broad. I was thinking that for an R/C oscillator entombed in parafin wax within a very solid steel/titanium case, the external temperature would eventually have an effect on its frequency and that a xtal/piezo filter may be in the R/C loop. Thinking in terms of manufacturing to meet the nominal frequency +/- 50Hz, I'd move away from an R/C circuit and use something less affected by temperature and voltage. The stuff I can find just quotes the tolerances without any schematics to back it up.
Wristwatches typically use 32.768 kHz quartz tuning fork oscillators. They are also very low power and survive modest shocks. I'm not sure they'd survive the shock and vibration specified for the recorders. Going the divider route with a higher frequency crystal uses more power for no practical benefit. The crystal is still vulnerable.
You can, however, find nice stable resistors that hold 0.1% or less over temperature. You can also find nice "NPO" ceramic capacitors that hold within a few dozen ppm/degree C. That's where the temperature variation would come from. Manufacturing tolerances of the capacitors would have to be in the 2.5% range or else trimmed with a parallel resistor for the R in the RC that is calculated and soldered in during manufacture. For reasons of cheap getting it within 1kHz or about 2.5% is "good enough."
After weeks of cold soaking there would be no further temperature inspired variance in the oscillator frequency. And there are oscillator circuits that are remarkably insensitive to battery voltage that could be used. So figuring out that they heard two distinct signals should not be all that difficult.
{^_^}