No, they should be honest and provide the information based on the complete frequency range. If they can deliver minimal 122 W (probably even less at 16 Hz) they should exactly write this. 250 W @ 4 ohms @1kHz doesn't tell anything as it doesn't have any relevance in real life - or are you always listening to just a 1 kHz tone? It is and remains misleading. I would never buy such a device. Never!
Chris, we've been having this argument for many years.
Until amplifiers are rated properly (not with dubious copypasta module datasheet specs) and reviewers test them against those specs, these arguments will continue. These vast numbers of inexpensive chip/module based amplifiers exaggerating their advertised numbers should be called out for their deceptive practices in no uncertain terms. No reccommendations for companies that misrepresent power outputs as people base their buying decisions on those advertised specs.
Interestingly enough, I repaired a little Teac amplifier yesterday for my father (some 80s piece of BPC he picked up goodness knows where, for a few dollars). 1kHz is always the reference level to start at and it hit its power output/THD spec easily. But below that, it was a disaster with one of the worst frequency reponses I've ever seen. Designed to roll off hard so as to not stress the power supply. It would have been sold with speakers that didn't produce much bass anyway, so it was a sensible, if not a HiFi decision.
But as always, if you don't like the protocol Amir uses, you can buy an analyzer, learn how to use it, and present your own results. I test my gear and repairs/restorations to my own standards. In some ways my tests are superior, in other ways not even close to Amir's. His testing is valuable, no doubt about that. Does it tell the whole picture? No way. Does it tell more than an online subjective reviewer? Absolutely 100%. Is it the gold standard? No.
But, ASR is free to view, read and comment on- that's pretty good isn't it?