A "startup" (according to Wikipedia and most others) is essentially a business in search of a business model (see Steve Blank's work in particular).
A small consulting business is not a startup, it's a small business that already has a perfectly fine business model. As soon as the founder picks up the phone and makes a few calls it's out of the "startup" search phase and is now started as a real business.
It's probably because I'm just a poor, unsophisticated non-SV type, but I never thought I was out of 'startup' phase in the consulting biz until I got my first invoice paid. But even if 'startup' is the hours or days between quitting your day job and hanging out your shingle, I don't see how it invalidates anything I said.
A small consulting business is not a startup, it's a small business that already has a perfectly fine business model. As soon as the founder picks up the phone and makes a few calls it's out of the "startup" search phase and is now started as a real business.