Why adverbs are bad

In the comments of the last post, WoollyBird asked why adverbs shouldn't be used in writing.

I think this is best shown in example. I've taken the liberty to take a paragraph from one of my favorite books, The Hunger Games by Suzanne Collins, and rewrite it with adverbs.

It's mayhem. The Careers have suddenly woken to a full-scale tracker jacker attack. Peeta and a few others have the sense to quickly drop everything and swiftly run away. I can hear stressfully called cries of "To the lake! To the lake!" and know they're hopefully trying to evade the wasps by hurriedly taking to the water. It must be closely located if they think they can firstly get ahead of the furious insects. Glimmer and another girl, the one from District 4, are unluckily left behind. They regretfully recieve multiple stings before they're even out of my view. Glimmer seemingly appears to go completely mad, yelling loudly and trying to furiously swipe the wasps off with her bow, which is pointless. She anxiously calls to the others for help but, of course, no one returns. The girl from District 4 limply walks out of sight,  although I wouldn't bet on her making it to the lake. I watch Glimmer suddenly fall, twitch hysterically around on the ground for a few minutes, and then go lay quietly. 

Now, read it as it's originally written:

It's mayhem. The Careers have woken to a full-scale tracker jacker attack. Peeta and a few others have the sense to drop everything and bolt. I can hear cries of "To the lake! To the lake!" and know they hope to evade the wasps by taking to the water. It must be close if they think they can outdistance the furious insects. Glimmer and another girl, the one from District 4, are not so lucky. They recieve multiple stings before they're even out of my view. Glimmer appears to go completely mad, shrieking and trying to bat the wasps off with her bow, which is pointless. She calls to the others for help but, of course, no one returns. The girl from District 4 staggers out of sight,  although I wouldn't bet on her making it to the lake. I watch Glimmer fall, twitch hysterically around on the ground for a few minutes, and then go still.

Now, which do you think is better written?
I suppose instead of treating adverbs like the plague, the better rule is to use them as little as possible. Here, Suzanne Collins does use two adverbs--"completely mad" and "twitch hysterically." But what adverbs do is slow down the reading. If strong verbs can be used instead, the writing comes quicker and the sight of what's going on is clearer to the reader. For example, which was better, "swiftly run away" or "bolt"? The strong verb "bolt" uses one word instead of three to describe the action of Peeta and the Careers, and does so with more power and action.