And according to PG, http://www.paulgraham.com/growth.html
My issue with charities being called startups is more in the for-profit vs charitable goals. Companies have goals that just don't jive with the goals of a good charity. If we take a definition based purely around 'designed to grow fast' yes it can fit. There's just more connotation to the word startup than the purely growth based definition Paul Graham puts forward.
addendum edit: There's nothing inherently wrong with the 'designed to grow fast' definition, it just doesn't sit quite right (with me) applied to charitable orgs because of the additional meaning I talked about above.
https://www.ycombinator.com/nonprofits/
> We’d been thinking about this for a while. We had a hypothesis that many newly founded nonprofits could benefit from the same techniques we use to help startups. We tested this with Watsi in the Winter 2013 batch and it worked wonderfully. They did all the same things as the other startups, including present at Demo Day (which is after all a room with lots of rich people in it).
> Since some people were confused when we funded Watsi, I’d better clarify that the money we’re putting into the nonprofits will be a charitable donation, rather than an investment in the narrow sense. We won’t have any financial interest in them.