What is the underlying concept behind Bandpass sampling?
Yes, the signal is changing "every nanosecond" for any non DC signal.  But if the bandwidth is really limited to 0.001 of the carrier frequency, then those changes are very predictable, as the changes result in a carrier waveform that is a nearly perfect sinusoid of a known frequency.  The signal can't differ too much from that highly predictable sinusoidal waveform unless the bandwidth is increased.  Assuming the bandwidth doesn't increase, any changes to the near perfect sinusoid are so small that one only needs to check the waveform every few hundred cycles of the sinusoid to see if it has drifted a bit from the expected point on the expected cycle.  Thus under-sampling at somewhere above 0.002 cf can tell you all you need to know in addition to knowing that the bandwidth was absolutely constrained to 0.001 cf or below.

But the sampling jitter requirement has to be on the order of a very tiny fraction of a nanosecond, or else one will completely miss the expected point on the expected cycle of the 1 Ghz sinusoid.