"That is something up with which I will not put." That quip, attributed (in various forms) to Winston Churchill, is the standard response to the claim that one must never end a sentence with a preposition.
The line between grammatical rules and grammatical customs can be thin. Is it ever acceptable to split an infinitive? If not, how would you edit "We are initiating a new training program to better prepare new employees for their duties"? Is "Ain't I a member of this team?" grammatically correct? Yes (if you accept "ain't," the only known contraction for "am not," as a real word), but who'd dare write it? The alternative "Aren't I?" sounds correct, never mind that no one would think of saying "I aren't." Likewise, they as a synonym for he or she has become so common that it no longer seems worth the effort to argue the grammatical incorrectness of using they as though it were singular.
Some people make the effort anyway; the "write like you speak" crowd and the purists (who insist that should be "write as you speak") can start wars over the most trivial matters. When one side is editing the other's writing, coworkers are well advised to stand out of the line of fire.
One might expect a blog called Good Writing Is Good Business to side with the purists. But the truth is, a piece of writing can be technically perfect and still be far from "good" on the average citizen's "worth reading" scale. There's a reason most popular books don't start out as graduate theses. While not generally caring to deal with businesses that sound ignorant, the typical client does want to interact with someone who sounds human--not like a computerized grammar checker or that seventh-grade English teacher nicknamed "the robot" by drowsy students.
If you write a press release that scores high on your word processor's readability scale but makes a newspaper editor yawn and toss it after two sentences, you haven't accomplished a thing.
No, you shouldn't write exactly like (or "as") you speak. Who'd bother following a blog that says "yeah" instead of "yes" and tosses in an "um" or "you see" every few sentences? But you needn't be afraid of using contractions. Or refuse on principle to start a sentence with a conjunction.
Or banish all one-sentence paragraphs.