It does, actually. They produces light waves in the IR range. This is where the heat comes from, not a dead-short or electrical rush type of heat more than the same wattage of any other product (all have some), so your application of that law is not applicable. LEDs have this too when power supplies and diodes get hot from electrons racing, but there is no IR, so less heat - it is also spread out over more diodes. If there was no IR, then 100W of MH electrons and LED electrons would be identical in hot power supplies and bulbs/diodes. For sure, some of the IR spectrum is not all that usable to most corals (if not all), but they are light waves nonetheless that took the same power to create the quantum.
I get where you are coming from, but it is misleading by those who have offered it before. Once you realize that the heat is from IR, which is wave/light output, then watt to watt output being equal starts to make more sense and then you can dial down to how much power being put into IR is wasted - there is some. This is where the inequality lies, but not as much as some think.
The only reason that they measure differently is the tools available for most to measure and the reliance on some using those tools as absolute - while they are the best that most have access to, a real manufacturer that can rent or use a good tool should not be relying on them. Or, they only measure a small piece of the spectrum - sure a light made up of nothing but 5.5k diodes will have more lumens per watt than a light putting out from 4500 to 7000 but only reading at 5.5k. Using an integrating sphere (usually about $20-30K) with all light sources at 100% output and capturing all of the waves, any light sources will have the same ratio of radiated watts to input watts. If you cut down the IR range over 720nm, then MH will waste 2-6% depending on the bulb since this is most likely useless waves that are pure heat.
In the end, if you have a real tool to measure, then a MH is 2-6% less efficient in useful spectrum than a LED (bulb dependent) - not nearly what people would have you believe. I never tested any T5s for their IR output since they won't fit in an Integrating Sphere. Here is where it gets crazy... to think about how even though LEDs have nearly all of their spectrum (power) in the useful range, how inefficient are they for growing coral since the concentrate their wattage on a handful of large peaks of spectrum ranges and leave huge gaps between. If you have to fill those ranges with other lights (most use T5s), then how wasteful is the excess output for that handful? I don't know to know this, however. This is a harder concept for most to grasp with more nuance and the "pro LED" folks can just say "heat" and people will get their somewhat off-basis argument.
I probably did a bad job explaining this... sorry. Basicly - 100W of "conservation of energy" heat will produce the same heat for any light source since it is dependent on electrons that are fixed - MH is hotter because of light waves in the IR range.