I can't believe there is even a debate about this. It is well known that driving a speaker that has a variable impedance curve that dips below 4 ohms with an amp that cannot produce the appropriate current at the low impedances will change the frequency response of the speaker. It's a well documented fact. If you can produce evidence to the contrary please do so.
If the amplifier is able to act as a voltage source at less than full power then the contray is certainly possible. For example the Osiris amplifier that @akg_ca mentioned can't double power at full power as load impedance is halved, but at lesser powers it can. In a case like that when the current demand is exceeded, rather than changing the FR the amp will simply clip.