Sometimes it helps to rearrange the sentence. His point is that you need no comma after "but." The "but" is integral with "there is still one chance of escape," and the phrase "if we are prepared to act promptly" is intersecting them. So normally, if you pop a phrase or clause right in the middle of another one, you set it off fore and aft with commas. However*, since there's a preceding independent phrase, we've already set that area off, so another comma right after "but" would be overkill.