The company deducts the expenses related to the truck because it belongs to it. However, your spouse’s personal use of a company vehicle is a taxable fringe benefit. The amount usually is reported as such on Form W-2. There is nothing for your spouse to deduct…the company deducts the business driving and there’s no deduction for personal commuting.
What a willing buyer would pay to a willing seller when neither is under any compulsion to buy or sell.