Sadly, "logical thinking" is of little use when it comes to interpretation of the IRS tax code.
According to the IRS, it is clearly "not allowed":
IRS Publication 526
"Mandy White owns a vacation home at the beach that she sometimes rents to others. For a fund-raising auction at her church, she donated the right to use the vacation home for 1 week. At the auction, the church received and accepted a bid from Lauren Green equal to the fair rental value of the home for 1 week. Mandy cannot claim a deduction because of the partial interest rule. Lauren cannot claim a deduction either, because she received a benefit equal to the amount of her payment."