"I received the spend-$500-get-10000-points, spend-another-$4500-get-5000-more points offer. Strangely, the offer implies that this activity will generate enough points to earn a free flight.

However, I am in the program that earns 1 point for every $2 spent. By my calculations, a $5,000 total spend will generate 2,500 regular points + 10,000 first bonus points + 5,000 second bonus points. That totals 17,500 points, not 20,000 points needed to earn a free flight."

You are mistaken...take a closer look. When you SPEND $500 (which gets you in return 500 pts) then you get 10,000 bonus points. (Total points at this point is 10,500). Then once you SPEND another $4500 (which will get you 4500 points) then you get 5,000 bonus points. THEREFORE, if you spend the $5,000 ($500 plus $4500) then you will have a total of 20,000 pts.