Startup: "...pre-revenue cash burning startup."
Business/company: "...solid profits, plenty of users..."
By this definition, most YC companies would be startups while 37signals/Fog Creek/Google would be companies. Incidentally, Facebook is still a startup by this definition, despite its size.
So like you say, the startup has to do whatever possible, because as I say, they're on borrowed time. They onus is on them to demonstrate that their idea and execution is accepted by the market ("Make something people want"). In a business with customers, profits, etc, they've done that and it's just a matter or managing what has been created. When you get to that point (especially when hiring non-founders), you have room to be flexible.