It’s correct for most modern power meters. They don’t measure power. Power meters measure material deflection and angular rotation and then calculate power. How much you flex (or heat, or make vibrate) a material with well-known properties can be used to estimate a great many things. That’s how your cheap digital scale works. Or your old stainless steel NSF thermometer.
Really? Power meters don’t measure strain, strain gauges do. Strain is then used to calculate force.
I don’t think many of the readers are very interested in us nitpicking about how power is calculated, right?
The point is that power from a double sided power meter is a measured value and not an estimate.
Reading this thread has me wondering how many of the TR crowd would train on a treadmill with a power meter than hitting the trails 
I too am a shadow of my former self… and it is hard to read tone online so don’t know if there is implied sarcasm there or if you are serious but I can definitely relate. My prime was 20+ years ago and I have avoided races for the simple reason that my ego couldn’t take that I am 15 min slower than my college 10k PR. So I needed a new challenge and just a year ago I got a new MTB as my injuries kept me from running regularly. I have found new life, am enjoying training and even jump in races when I can. The bike has lit a fire I didn’t think I’d see again.
So if you were serious don’t give up. Have fun and enjoy the ride!
Definitely serious. I have run some races of late, just because my wife wanted to do them together. It’s depressing to be a minute/mile off where I was 10 years ago. But I think I’ve accepted it. I don’t see myself racing on a bike. Too complicated and too dangerous. At least in a running race I know what I’m doing.
Strictly speaking, it’s a calculation based on a measurement and some assumptions/estimates. A single-sided PM just makes one other (quite big) assumption.
Thanks for the answers everyone, I certainly learned a couple of things.
For the record, the Coros watch is pretty good so far, having a power figure has been little more than a gimmick for me so far but it’s early days. It’s handy to see where I was pushing harder on hills and trails, versus flat tarmac - more effort for the same speed etc. But for actual training efforts I still go on pace, HR and RPE.
Single-sided PMs could get around that other quite big assumption if they just skipped the doubling: they could just report the left leg. The manufacturers (and people who buy them) say, “accuracy doesn’t matter, only consistency” so stop doubling the left-side. That’s more honest.
Congratulations of your running ability. I have a friend who is sort of similar to you: he was a cross-country runner and says that he could never achieve the same results on the bike as he did in running; nor could he achieve the same HR, leg, and lung “burn” that he’d ordinarily feel in training.
That said, this is a rule of thumb to estimate run power, not equivalence between running and cycling. There is a rough correspondence between power in running and power in cycling but the relationship isn’t exact: I brought the rule of thumb up on Slowtwitch several years ago and although many ST’ers said it was close, there were a few who, like you, said it wasn’t. Mostly, these were people who were “primarily” runners who said they couldn’t approach that power while riding. I’m the other way: I gave up running years ago after a series of injuries so I’m pretty sure I can’t run worth a damn even if my aerobic system would handle it.
If you want any further evidence that run and bike power can not be compared my best 20 minute powers are
20m run power is 391watts 5.32 w/kg,
20m bike power 295watts 4.25 w/kg
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