No!!
I have repeated on forums about such internet hearsay, misconception..., the fact is, it depends on what kind of "support" ones mean, or want, in terms of driving such low impedance (lower than 6 ohms nominal) speakers.
Most AVRs, unless they have a impedance sensing device such that it would activate the protection circuit, will be able to drive 4 ohm, or less speakers.
For example, the Sony is rated as follow, pasted right from the Owner's manual:
Amplifier section1) Minimum RMS Output Power (6 ohms, 20 Hz – 20 kHz, THD 0.09%) 100 W + 100 W minimum
That means it should be able to deliver about 4 A, with 2 channel driven simultaneously.
It also mean, from Ohm's law and the power formula calculations, that it could do 64 W + 64 W minimum into 4 ohms, or 32 W+ 32 W into 2 ohms.
No electrical engineers, or anyone with basic EE knowledge would dispute such a fact, again, assuming the AVR does not have impedance sensing to activate some sort of protective circuit.
In general, if one wants to make a blanket statement, then as
@dlaloum mentioned many times, it is not a good idea to use AVRs to drive 4 ohm nominal speakers, except for those flagship class AVRs. But then, it would not be a good idea to rely on "blanket"/generic statements either, because it still depends on a few other factors such as distance, speaker sensitivity, listening habit, and the speaker's so called "power handling" specifications. The last one cannot be ignored, think about it, if your speaker manufacturer specs say recommended amp power, or power handling 15-150 W, and rated 4 ohm nominal, and then your drive it with a Crown amp such as the XLS2502 at the highest gain setting, you may risk damaging the speakers unless you are very careful with the volume control, such as keep the remote and the volume inaccessible to small kids.