For example, if a function generator has a minimum load of 1kohm and a maximum load of 50Mohm, if we connect less than 1kohm, the output amplitude will distort.
But what happens to the output waveform if we connect 60Mohm?
Most of the function generators' output impedance is \$50\Omega\$ and they give rated terminal voltage only if they are terminated with a \$50\Omega\$ load. So any other load connected to function generated gives amplitude different from that of the displayed.
Some function generators support 'High-Z' mode in which displayed voltage is delivered to the load if the load resistance is greater than a minimum rated value. But I guess there is no upper limit for the load resistance in such cases. You will get undistorted output if you connect a \$60M\Omega\$ resistance. Where did you see this?