If you read through the whole article and the comments, the author adds more nuance to this advice than the title suggests.
It boils down to "shopping your terms verbally is fine, just don't flash your actual physical term sheet around town."
Hm, I distinctly recall reading:
Also, don’t shop a verbal offer.
OTOH, if you're not hot, they will use any lame excuse to walk, and you won't have anything to 'shop' in the first place, other than warm fuzzy talk at the end of an expensive lunch.