If a company or individual unrelated to you (e.g. not your employer and not a relative) either gives you a car for free, or sells it to you for $1, with no expectation of anything in return (i.e. not a trade or barter), the only tax obligations are on the actual sales price: the seller must declare they made $0 (or $1) on the sale, and perhaps collect sales tax on the $1, but you as the purchaser are not obligated to pay anything else.
If the seller and buyer are related, tax obligations are different because it involves a gift or implied compensation, but that's not what we're talking about here.
So it is indeed possible to pay no more than $1 for a car. As for registering the title in your name, that's a different story, and has nothing to do with the actual sale.