You only need concern yourself with three words in the rules. These three words leave absolutely no room for interpretation.im not taking this out of concept, as i have read your entire post, but it seems that unless someone posts the actual law as its written in the law books, here, everyone will continue to have their own idea of what the facts are, BECAUSE there are so many places on the internet that have a bit different interpretations posted by authoritative people....
im not sure that this is the explanation of the actual law as it is written in the books, or just someone elses interpretation, but I have personally this read in a marine "rules of the road" manual, that regardless of why the engine is running, if you are under way and the engine is running, you are considered to be under power. period.
the explanation given there was was because its assumed by the law that so many people will be tempted to engage the transmission when the engine is running and charging batteries so that they can take advantage of the otherwise wasted power, and in addition, with the engine running, you have the ability to out maneuver and better avoid conflict with the other vessel at the shift of a lever.
and it may also be assumed by the law, that if there is an accident with a motor sailing vessel and a non motor sailing vessel, any argument that is given as to whether the yacht was actually under power cannot have the excuse that it was only running the generator and not actually in gear...
it is a fine line between "what it is" and "what it appears to be".... I think the reasoning here is to take any excuses or temptations out of the equation.
but none of this makes a difference or care unless you are situation where there is a close call and you are either the cause of it, or you take the advantage at someone elses expense, and it is found that your engine was running and available to prevent the situation...
"PROPELLED BY MACHINERY"