I definitely agree, but with one exception: a fair amount of these companies have reached such a scale that they actually have to invent or at least develop new tech in order to run their business. Facebook and Twitter, for example, aren't primarily "tech" companies, but because they operate at such an insane scale, they regularly develop new tech that allows them to continue and grow. So the tech part is more or less vertical integration - not their primary business, but also definitely not negligible in terms of innovation.
I guess the question is: how close does technology R&D need to be to the core business to be a "tech" company? I don't have a good answer. Major automakers dump tons of money into R&D, but we'd never call them tech companies.