Not necesarily true
You should be able to use a 6 speed freewheel with 7 speed index, you will however need to adjust the upper limit screw of the derailleur so that seventh click doesnt throw the chain into the spokes. If the rider is using down tube shifters that can be switched to friction mode then he may possibly be able use 6 or 7 speed gear set...though the use of the 7 speed gear set with 6 speed shifters may be limited by how far around the DT shifter will go.