As Doug says, it was a great advertising slogan by Browning. It was very popular with quail hunters down heah' in Mr. Bob's heyday.
As for the 16, as a gauge, it has a place, but IMO it is limited. Before flaming me let me explain what I mean. I have a very "sweet" 16, a 32" L.C. Smith, that I use for late season doves. Now, I admit that a 32" 16 ga. is very specialized. I use it for high flying doves, and nothing else.
I believe that a shooter who has multiple (gauge) guns should apply them as best as possible. I begin dove season with a .410 S x S, and also use it for early release (August) quail. After the first week or two of dove season the birds wise up and start flying higher, and are more evasive. They learn quickly. I then switch to a 20 ga. for doves, with 7/8 oz. loads. Both the .410 and the 20 are gracious plenty for their quarry at the time. Late in the season, when the big migratory doves move into the peanut and corn fields I may use the 16 with 1 oz. loads and full chokes. Works really great. I am a serious duck hunter, and believe they deserve to be killed with all expediency and surety. Therefore, I use only a 12 for them. If I knew the only duck there would be teal, I would feel fine using a 16 or even a 20, but I don't have the luxury of knowing that. So, I use a 12 ga. 3" load of steel 2s or 3s, or bismuth or tungsten 4s.
All this COULD be accomplished with a 16, I guess. But I am convinced there would be many more duck cripples. Steel is marginal enough at best, especially when you pass 30 yds., even with the heaviest 3" payloads. I just can't feel comfortable using a lighter load, intentionally, even over decoys, which makes up most of my duck hunting. The one other application I can see where a 16 would be perfectly fit, beside for teal, is shooting woodies in a small beaver pond. A quick handling, open choked, 16 would do that job just splendidly.
This is all just my opinion, after many years of using them. I would never chastise a man for choosing to use a 16 for big ducks, I just probably wouldn't understand it.
SRH