No, your understanding is not "okay." It is not surprising that you found one source, which doesn't have a date on it, to support your "understanding" while ignoring all of the more recent sources which state that normal tipping is now 20% (and has been for many years).
Many restaurants have a cheat-sheet at the bottom of the bill showing how much is 18%, 20%, etc. Over the last few years, many of them have done away with showing the 15% option, because it is considered below average at this point.
The fact that you are trying to defend your stance between 15% and 20% on a damn dinner bill shows how cheap you are. On a $50 dinner tab, the difference is $2.50 between the two. If you're so god damned worried about $2.50 so you can be an "average" tipper, I suggest skipping the appetizer or ordering water instead of soda so that you can truly be average (by most accepted standards today).
Why anyone would not want to be generous (and by "generous," I mean a few extra dollars) is something I cannot understand.
I give the same shit to colleagues when we have hotel stays. Almost all of them never tip the hotel maid who cleans your room and makes your bed each night. If she cleans 40 rooms per day, if everyone just gave her $1 (which is average to below-average), that extra $40/day pays for her rent each month. She isn't getting rich being a mad. Spending an extra $1 each hotel night might come out to $20/year for the average person. You won't notice it at all.
Oh, and you screwed the waitress last night, too. Way to be a cheapskate.