And gets the answer wrong.
Schmitt makes a reasoned argument for whom as a possibility, but because he builds his argument using a different sentence, his conclusion doesn't apply to the original.
In the following sentence: Harold prefers contestants _____ he can sense are facing him.
Which would be the preferred relative pronoun?
Traditionally, who is used to mark a relative pronoun that served as the subject of the adjective clause and whom was used to mark a relative pronoun that was an object. Thus, we have “That is the man who gave the argument to the English and French to tell President King,” where “the man” is the one giving the argument. We also have “That is the man whom I saw coming out of room B,” where “I” am seeing “him.” In this respect, we could equate who with he and whom with him... so we could complete your sentence as “Harold prefers contestants whom he can sense are facing him,”
The sentence used in the explanation, That is the man whom I saw coming out of room B, has the embedded clause I saw him coming out of room B. This would have been analogous if the original question had asked about Harold prefers contestants _____ he can sense (them) facing him. Unfortunately, the original sentence was Harold prefers contestants _____ he can sense (they) are facing him. In other words, whom is not a possible answer [update, March 4: I don't mean to claim that it is actually "wrong" to use whom here, just that following Schmitt's logic, the answer should be who. See Arnold Zwicky's lengthy Language Log discussion, section 9.2 in particular.]
And so it goes.