I get pretty annoyed by Sinek's schtick because the terms he picked are so ambiguous (unsurprising for people into bullshit science) that it's hard to know if there's more to his theory than obvious business bromides.
If by starting with the why, you mean starting with the purpose, I think it mostly makes sense. You have an end in mind, a vision, and from there derives a set of products (means to that end), and the target customers are going to be the people who subscribe to that vision.
Couple problems with that:
a) "Why" is also often mistakenly understood to have a causal or motivational sense: why did people start that company? Why are you doing that? Those things might have nothing to do with the purpose of the company itself, if it has any. It could just be that the founders felt like doing something.
b) The vision of the company, and what it delivers, could just as well be described as a "what" than as a "why". The functional benefits of the product are what people are buying. The products (means to the benefit) are the "how".
Basically, every term he uses can be reinterpreted differently and still make sense, which causes more confusion than clarification every time this topic is brought on the table.