And for another, I think authenticity is a theoretical notion that should be applied very thoughtfully or not at all. South Asia has had chilli peppers for only about as long as Italians have had tomatoes, the Irish, potaotes, and the Belgians / Swiss, chocolate, i.e. five hundred years. That's also about as long as -- perhaps a little longer than -- sugar has been widely used in most parts of the world. If we consider some foods as "authentic", "typical", or even symbolic of a culture today, it's worth also considering that, at some point in the past, they were new-fangled, upper-crust, weird, fashionable, experimental. In India, "chai" has an even shorter history as an item of mass consumption.
Innovation has always happened, and it's not inherently good or bad. Following a recipe precisely in order to be "authentic" suggests a lack of creativity, even though the skill may be evident. It's like a shagird singing exactly the same taan as the guru -- it speaks of poor training, the teacher's tyranny, and the student's lack of imagination and confidence. Besides, I don't think a specific recipe can be "authentic" -- even your grandmother and her sister would not cook the same thing quite the same way. What can be considered authentic or traditional (for want of a better word) though, is the idiom -- the way in which we might adjust, innovate, omit, or substitute. There's some predictability to that, based on the dominant notes we're used to, and the flavors we're exposed to. When someone talks about a cuisine, I think of the idiom. It would not occur to an Indian to add vanilla to chai, because vanilla is just not used in Indian cooking. So adding vanilla and steamed milk to chai is okay if you like that sort of thing, but I think it's misleading (or miseducating an uninformed public) to call it "Indian chai". Oh, and please nobody say "chai tea" unless you would also say "pizza pie", "pita bread", and "jeans pants". "Chai" is tea; no need to say it twice-twice. (Non sequitur: wish I could find the comic strip in which a dis-Oriented new age type was sipping a "Tai Ch'i chai tea latte".)
And misrepresenting others' cuisines appears to be a universal problem: we're guilty, too. I remember being surprised the first time I was served real espresso in India. It was well into my adult life, and the host was Italian. Each guest was asked if he or she would like tea or coffee. I chose coffee. What arrived was even more bitter than it was tiny -- but delicious! Until then, there had been an inexplicable conspiracy, at least in the India I inhabited, to pass off an eight-ounce, frothy, latte-like beverage as both espresso and cappuccino. If real espresso came in eight-ounce cups, many really laid-back Italians I know would be bouncing off the walls.