I don't see how it's true, but it's apparently true, I have read in places, and there are a few posts up there... that say that decelerating while in gear gives you the best possible fuel economy.
regarding engine braking, I use it for the most part on hills and freeways, I have to drive down a grade when coming home from work, and if I put it in neutral my car will easily pass 85 going down that hill, but put it into 5th and just lay off the gas and it does a perfect 70 mph, so I save gas and I save my brakes (and I save my kidneys too because I have a midly warped brake rotor I haven't gotten around to replacing)
I don't use it in regular city driving though.
Oh and regarding that post on downshifting into 1st, most manual tranny cars have a limiter built in that won't allow you to do this until you're under 15 or 10 miles an hour to prevent the engine from redlining, plus the collosal magnitude of the jerk it gives you is so bad you normally don't ever try it again anyway.