Sadly, they can. I went through something similar on a new ICE car. Went to the dealer, found that the car I want is in transit to the dealer, spent couple of hours negotiating, we agreed on the price, signed a contract, I put down a deposit, car was supposed to arrive in a few days. A day or two later, I get a phone call that "the sales manager made a mistake, and the price is 10% higher". I spoke with an attorney and it turns out the dealer association over the years has sucessfully lobbied for some great laws to car dealers - after signing the contract I am the only one obligated. The dealer can refund my deposit and sell to someone else up until they hand me the keys. On the other hand, if I wanted out, they could actually sue me for the entire price of the car (though typically they would just keep my deposit and move on).
So, while Tesla and NADA and not friends, it doesn't stop Tesla from benefiting from laws paid for by NADA.
Ps) I complained to Toyota corporate about the aforementioned dealer experience, they told me they can't force the dealer to honor the contract because they are independent from Toyota, but at least they offered me $500 cash if I still bought a Toyota at any other dealer, which I did. Tesla being their own dealer, there would be nobody to complain to.