No. Most startups are designed to grow fast. But many non-startups are designed to grow fast. There is overlap in the Venn diagram, but they are not the same thing.
> If Ray's original plan
If that was Kroc's plan, you'd be right. Do you have some evidence it was?
As far as I can tell, he spotted an existing restaurant that had already found product-market fit and just scaled the operation using variants on known franchising approaches. I also haven't seen any evidence that at the time he foresaw suburbanization, white flight, and the resulting increase in value of heavy branding, trends that were nascent at the time he joined McDonalds.
I'd say it was more akin to the top-growing restaurants of today, ones I point out elsewhere in this discussion. They are fast growers, but they are scaling mild variations on well-known business models.
To this day this is a major selling point. When travelling you can take your chances on a local place or go with what you know.
That's what "a company designed to grow fast" is.
>You can have a rapidly growing company with an old business model. Look at McDonald's"
McDonalds was a startup under this definition. If Ray's original plan was to take an old business model, redesign it for cars, and scale it rapidly with TV advertising, that's a startup by Steve and Paul's definition.