In the world of startups, 'pivot' is just a fancy word for 'our original idea didn't work.'

Well sometimes that's not true...sometimes an idea partially worked and needs just a tiny tweak or two!

Yes, and that's great! In my understanding, a startup is NOT a business. A business is a structure with a "stable, profit-generating operating model". A startup is a temporary structure that is needed to find a “stable, profit-generating operating model.”

Correct but there's nothing wrong to admit and acknowledge that original ideas can go wrong sometimes.