I agree with this, though since there are probably lots of fiction-writers here as well, I want to point out that for fiction the advice is somewhat different. In fiction, you'll want to replace adverbs with something longer, because an adverb is telling and not showing, and you need more words to show something than to to tell something.

To quote Techniques of the Selling Writer:

Whenever practical, substitute action for the adverb.
"Angrily, she turned on him"? Or, "Her face stiffened, and her hands clenched to small, white-knuckled-fists"?
"Wearily, he sat down"? Or, "With a heavy sigh, he slumped into the chair and let his head loll back, eyes closed"?
Vividness outranks brevity.
At least, sometimes.

This isn't always a bad guideline for non-fiction writing, either. Telling requires the reader to rely on your authority; showing lets them see for themselves. Compare just saying "biologists romanticized evolution" with giving an example of insects defying biologists' expectations by turning into cannibals.

Of course, on some matters you should just state an issue with your authority and get on with it. If you're explaining confirmation bias, no point in launching to a digression about how and why the brain is composed of neurons. Skip that, or if writing online, just provide a link.

Vividness outranks brevity - at least, sometimes.