Not saying she was a liar, but......
Also, interesting to know they went through crossing unlike any others. Others have those pesky border patrol agents. Wow! I am impressed!
That story doesn't pass the smell test. So what if they write down the VIN number wrong, they have all the driver's licenses and vehicle plate numbers to work from. Sounds like an urban legend to me, and not a very good one.
Having a contract emailed to you absolutely in no way obligates you to anything. When the dealer started making noises about changing the price, any previous contract discussions are null and void and a new contract would have to be agreed on by both parties.