I don’t think “there is a class difference between those who are self-employed and those who employ others and describing both as business owners only flattens that difference” is a reach. Describing oneself as a business owner instead of a laborer when doing freelance labor is an example of the tendency of the lowest of the petty bourgeois to try to liken themselves to the “haute” bourgeoisie.

I am attempting to explain what OP said in the title.

people’s brains are so addled by capitalism that people who take pictures of people’s pets for a living will tell you that they have a “pet photography business”