Coasting in Neutral Does Not Save Gas

To be clear, coasting while in gear still saves gas.

I've heard this before, and I understand how cutting the fuel supply to zero would save gas, but there are a couple of things that I don't understand:

Wouldn't this mean that coasting down a long hill in gear would cool the engine and in particular the catalytic converter, potentially causing some operating hiccups and a big emissions spike when eventually reaching the bottom?

Why would built-in mileage computers, with direct access to actual fuel injection figures, compute gas mileage from some other measurement that's only theoretically related under some circumstances? Isn't that sort of going out of the way for worse results?

I've been seeing a bit of this type of article lately, perhaps due to the fuel prices rising, and have wondered; if this is true, why do I continue to hear exhaust noise when coasting in gear?

Exhaust noise is purely the sound of detonation, which requires fuel. So why do I hear it if there is no fuel being used?

I'm open to the possibility of my brain faking me out and I'm NOT actually hearing it, too. But I'm pretty sure I am. (NB: My car is a 1995 model, but it is fuel injected.)

what worries me is that the title of the article is 'neutral does not save gas' and not 'neutral is exceptionally dangerous because you are not in full control of your car'. if something jumped out at you and you suddenly needed to gas your car, you just lost 1-2 important seconds (if you're very good at remembering what gear to hop into for a given speed/rpm). the next stupid thing you could do is "I'm coasting so I might as well turn my car off". now you lost power steering.

no, neutral does not save gas. your fuel pump has a idling injection setting (lets say keeping the engine at 950rpm). when you're in neutral, the injection mechanism switches to that rate, and you slow down by friction (bearings, wheels, transmission, weight, etc). whereas if you're coasting in gear, the engine switches into engine braking, and eventually slows you down without using fuel. in gasoline engines that works by creating vacuum in the engine (which slows the movement). in diesel engines that vacuum is not created, so the exhaust is somehow blocked (again, slowing the movement).

HUGELY oversimplified explanation, I realize. with apologies to actual mechanics. I'm just a nerd who hammers at his car :)

I think this idea comes from when most vehicles had carburetors rather than fuel injectors. If fuel consumption were driven by airflow into the engine rather than electronically controlled, I imagine there would be some benefit to coasting in neutral.