I've worked for two tech companies doing fairly cutting-edge R&D that were definitely "start-ups" in every sense of the word, called themselves such, but were never developed with the intention of getting a bunch of VC money then making a big exit. These are much more common than you probably realize, even within the tech sector.
Getting really big then exiting basically necessitates that you have to be in a mass-market business. But do only mass-market businesses get to call themselves start-ups? Is there no place for start-ups in specialized fields with significant revenue potential but without the kind of universal applicability that makes VC's wet their pants?