A small business was once a startup. Startup doesn't have to mean explosive growth and a quick sell, it can also mean long-term sustainable growth.
What you described (long-term sustainable growth) is the hallmark of a good small business. And there is nothing wrong with that! But it is a very different model from what we know as a "startup". After all, if "startup" could mean any small company, there would not be any reason to have the word at all! We could just say "small business" instead.
The two models are very different in every way apart from the size of the company. Having different words for them just makes sense. It's important not to see this as some judgement on either concept; rather, it's just using language to differentiate between two fundamentally different things.
Just look at Instagram -- it was created by some guy fishing for a way to game the system, and lo and behold, it worked out for him (after failing with some ridiculous whiskey startup idea). What Zuckerberg did for Instagram was self-serving charity: he essentially used a billion dollars worth of capital to perpetuate the startup bubble (think of how many MBAs are going to flock to California now hoping to become the next Instagram), which only helps Facebook in the long run (once the bubble pops, no one's going to be buying ads from them anymore).
Any reasonable businessperson would see a company like Instagram for what it is: a server with some data on it. UI? Number of accounts? That's all irrelevant: the revenue was exactly $0. Even SEO scammers selling private label goods off of Ali Baba are more financially viable than them!
The problem of defining 'what a startup should be' is that you end up in a situation analogous to a doctor treating a patient's symptoms rather than the underlying disease. The idea that your company needs to have explosive growth and be reachable by x number of people and have a valuation y dollars means that the CEO is usually running around spamming his product everywhere, taking out huge numbers of ads, and schmoozing with VCs instead of doing what he should be doing -- developing a financially viable product that customers want to use.
I think you mean technical person, because a business person saw them correctly and acted accordingly: a threat (and this is all about growth, and this is the reason of separation between startups and regular companies).