I’ve found ultimate proof - quotation from 
“Fixed an issue with Beronath, Reforged’s Elemental to Physical conversion not applying to Elemental dots (Burn, Frostburn, Electrocute).”
This is from 3 years ago.
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Yep, thanks for the link. As I said, I stand corrected. Maybe it wasnt converting at some point in the past and it got changed. I unfortunately still believed it hadnt changed. I have been playing a lot longer than three years… 
No problem. I can see it being misleading since the conversion
Fire -> Lightning
does not suggest the dots are converted.
And also stuff like Fire to Aether (here the dot doesn’t disappear but I remember there was some wierd thing with multiple conversion to dots when the sum of %'s exceeded 100% if I remember correctly but don’t remember the details).
Anyone remember if the stuff in bold below is still a thing / was a thing?
I think that for Dots 100% Fire to Aether and 100% Fire to Lightning might leave you with just 50% Electrocute because Aether dot doesn’t exist wheras it should leave you with 100% Electrocute. With Flat there’s no problem - 50% Lightning 50% Aether
Because conversions formulas are the same for flat and dots?
In other words conversion to non-DOT type lowers your DOT if the sum of all conversions exceeds 100%
Or the double buff you mentioned above.
I mean I once assumes/get an impression DoTS are not converted, his/her mind can find some things that might confirm their belief.
There is a very useful thread about conversions:
Still trying to figure out what the hell Freeze Damage is. Im guessing this is just a mistype and whats actually meant is Frostburn damage?