The argument being made is a rather poor one. In the example given, the waiter walked 10 feet to you, I would agree that you shouldn't have to tip.
I'm ambivalent on tipping culture, if we can institute a fair minimum wage then I'm fine with getting rid of it, if not then shut up and tip. All that said, the things we tip for has gotten way out of hand. Tipping used to be 15% for good service while some people were giving 20% because prices had remained low. Now with food prices increased businesses and wait staff are encouraging 20-25% and tipping options are being added everywhere.
My rule of thumb now is 20% for standard wait service (taking my order, bringing my meal, refilling beverages, and cleaning the table afterwards). If any of those elements isn't being fulfilled then I do not give a percentage, though if someone is going around filling drinks I'll probably leave a dollar or two. I also don't give a percentage tip for drinks that don't come with free refills, instead I will calculate the 20% tip without those beverages (typically alcohol) and then leave $1 per drink.