I think it depends upon whether or not you wish to look at it from a welding engineer standpoint or an electrical engineer standpoint.
In other words, nobody ever really believed that the existing formula for heat input calculation is accurate in an absolute sense. It just works from a practical standpoint(not that methods cannot always be improved to some extent). Much like Charpies and Tensiles.
I did a quick scan of the article and think it indicative of the current state of the debate. The conclusions are valid when definitions, functional definitions typical of scientific experimentation, are defined a certain way.
So, after blathering all this rigamarow, I'm guessing the majority are calculating the ratio of peak times to background times into the final results for heat input.
Is this absolutely accruate? Probably not. Is it close enough? I'm thinkjing form now that it probably is. And then some.
I once watched a gentleman by the name of Harry Ebert (some of you may have the priveledge of knowing Harry) sit through a most excellent 'research' presentation at the AWS show in Detroit a few years back. And nothing of a theoretical nature will be lost on Harry. But he stood up and asked the question at the end of it: (and I paraphrase) This is all well and good but how does this translate into a practical application? The presenter was at a loss to answer.
Sometimes we get lost in very fine technicalities of theory when something more practical is all that is needed.
In my opinion, all the fine detail of theory involved in this debate have yet to prove themselves enough to be applied in the shop.