That may be the FAA's definition, but if pilots just used that as a guideline, there would be an increase in icing related accidents. Icing in clear air with better than 1sm visibility happens all the time.
This on the basis of what, then?
Icing in clear air happens all the time? No.
Icing in the presence of large supercooled water droplets happens all the time? Yes. However, large, supercooled water droplets aren't found in clear air. They're found in condensation, and in visible moisture.
Do we know the cause of the reduced visibility in the case in question? Reduced visibility of three miles in smoke...causes icing?
You can factually state that an increase in "accidents" will occur based on not using engine anti-ice when operating in accordance with the manufacturer guidelines and intructions? Whereas the manufacturer (and the regulatory agencies that over see the manufacturer) operate on the basis of extensive experimentation and research, and more than a significant database, what's the platform for your own research that dictates otherwise?
If any pilot thinks they must be in "precip" of in fog with vis less than a mile, to have icing, their days are numbered in aviation. And if/when that day comes up, hopefully they're flying single pilot with no passengers. I've flown with enough different pilots through the years, hundreds of different pilots, they all use anti-ice systems in pure IMC and in the clear with low vis, near freezing temps, smart decisions on both counts.
We're discussing a circling approach in three miles visibility with a temperature above freezing.
We're now to believe that the basis for making up your own policies and rules (as well as apparently statistics) is that you've flown with "hundreds of different pilots." Setting aside that your own obvious lack of experience from your language and statements tends to devalue your baseless assertions, your basis for making these statements is what you've seen others do...not what you do, and not what you do based on acceptable or approved data. Enlightening.
Flying on the edge is hardly 100% safe operating practices. There's no such thing as 100% safe anyway.
Perhaps you should get out of aviation then. Even the practical test standards require that you complete any maneuver with the outcome never in doubt. If you have doubt, and believe that no operation can be made safely, then it would appear you're the one placing yourself and your alleged passengers at risk.
You really believe that flying a circling approach in 3 miles visibility is "flying on the edge?" I have to wonder if you've ever seen the "edge." I've spent a great deal of my career operating right about where the edge is, and on many sides of the "edge," and I can tell you that flying a circling approach in 3 mile visibility isn't it.
Our AOM uses 10 degrees C Total Air Temperature as the temperature base for use of anti-ice in flight, be it nacelle anti-ice or wing anti-ice. Out TAT probe isn't sampling only ambient temperature, but ram air temperature rise, too. Icing conditions are 10 deg C TAT with visibible moisture of any kind: clouds, fog with visibility of one mile or less, snow, rain, sleet, or ice crystals.
I too fly with hundreds of pilots, right here, and every one uses the aircraft operating manual as the guidance by which anti-ice is applied. As do I. Perhaps you believe that my time in aviation will be short, as a result...you've not provided any rational basis for that statement, but you can believe whatever you want. The airplane has been operated for many years, a number of decades now, and hundreds of thousands of flight hours, on this basis...and will continue to be operatedon this basis...whether you agree or not.