Another word for authentic is believable. Meaning the consumer can believe what the brand is communicating about itself, its products and its culture. Apple appears authentic because they demonstrate how their products simplify life and make it more enjoyable. Honda expresses reliability and fun, and their products are certainly known for reliability. Look at struggling brands, like Sears, who tried to be all things to all people, from Craftsmen tools to Lands End. It was too broad and general, and the market validated it with declining sales.
I'd say most leading brands are good because they resonate with people and ring true--which I would say is authentic.
Have a Coke and a smile. Powerful brand. Very simple. Is sugar water authentic? Perhaps not. But do people enjoy Coke, and does it convey happiness? I think so.
Nike Just Do It. Very authentic. Nike was born from competition, and has corporate goals to crush the competition -- so this is a brand ethos as well as a rallying cry.
Authenticity can also mean living what you say. So Tom's Shoes--donating a pair of shoes to a person in need for every pair they sell. Pretty powerful stuff.
Having worked with Ikea, I can relate first hand that "Creating a better everyday life for the many people" is absolutely a core value. Their furniture may be quirky and varied, but somehow they build stuff that fits our needs at various life stages really well, and also create a truly unique store experience.
I'd say authenticity is the first step to creating a brand. I view my role in helping companies discover their brand, not in creating the brand. Brands exist. Every company has one. They are frequently hidden, or surrounded by layers of complexity. But the key to branding is finding something an organization IS, then being that really well.