This is not strictly true. You can reproduce a band-limited signal as long as the bandwidth of this signal is smaller than half the sampling frequency.

For example, a signal that only has energy in the range of 9MHz to 11MHz has a center frequency of 10MHz, but a Bandwidth of 2 MHz. You could sample, and reconstruct, the signal perfectly with a sample-rate higher than 4 MHz. Any content between DC and 9MHz that would be present would distort the sampled waveform, though, and create artifacts.

https://en.wikipedia.org/wiki/Undersampling

Of course, nowadays most often one just uses a very fast ADC, and one can then choose a suitable sub-band by decimation (in a FPGA or ASIC), a kind of digital frequency filtering.

Undersampling was often used in older RF gear (and, maybe it still is for reaching the hightest frequencies? I don't know what's the current state of the art).