Tax law 101: You cannot turn a transaction for a product into a pair of "gifts" between the parties. Where both parties are subject to contracts for services or payments, there are no gifts. Similarly, all "gifts" from employers to employees are considered non-gift income.
A car given to an employee as a "gift" is income to the employee and a taxable deduction by the employer. See Duesenberg (I'm trying to find the citation. I only remember that it involved an expensive car given to a senior employee in the early years of US income tax.)
And there is an Andy Griffith Show episode about this, about Aunt May having to pay income tax on prizes. The tax man was played by the guy who played the priest on MASH.
"While in Hollywood, Aunt Bee wins several new appliances on a TV quiz show, but when she returns home she loses her friends as a result. William Christopher plays the IRS agent who visits the Taylors to collect taxes on the prizes."
https://en.wikipedia.org/wiki/List_of_The_Andy_Griffith_Show...