You heard right: the energy difference of nuclear spins in magnetic fields is very small. If you apply the Boltzmann distribution to such low differences, you will find that the low and the high energy state have almost equal populations which gives your spectroscopy very little material to work with. In radiation-matter interaction, the coefficients for stimulated emission and absorption are the same, so the radiation output difference is very small.
That is also why you usually perform pulsed NMR, not dispersive NMR measurements.