Improving RF sensitivity
Common sense tells me that if you're listening over a larger spectrum,
  the radio has less time to distinguish between signal and noise. But
  that's not a satisfactory scientific answer, is it?


Your common sense is flawless. A generally accepted formula for receive sensitivity is: -

Sensitivity = -154dBm + 10\$log_{10}\$(data rate)

So, at 1Mbps the receiver's best sensitivity is -94dBm. For 1kbps this becomes -124dBm.

There are several factors that go into this including temperature of receiver but at or around ambient this formula is pretty useful. Temperature produces noise and background thermal noise is ultimately what you are fighting against (plus interference from other transmissions).

If you want more theory, then the essentials of radio wave propagation is the best source I've come across. See page 14.

To make use of the higher sensitivity, a receiver's bandwidth has to shrink to suit the smaller bandwidth of a lower baud rate transmission.