IMO Google adwords employees do contact customers directly out of the box. Once I got a letter in my house addressed to me which also had my google account id offering me free adwords credit.I really really don't know how that person got all those details. I hadn't even heard of adwords during that time. But when I use the free code in that letter, it worked.

I also saw similar incidents with my friends and also one friend had also received a similar email to what you have received. If you had been using email for may years, then I am sure you will know how to tell spam from ham Good luck to you with your offer