Congrats on your pregnancy!
Progesterone, a hormone produced by your body after ovulation and throughout the first trimester to support a pregnancy, can raise your blood platelet levels. Having elevated blood platelets can cause clotting, and will cause you to test positive for a clotting problem. So, it is quite possible that all of the tests were correct. Baby asprin is commonly referred to help with this issues, even during pregnancy. If your doctor feels that this is in your best interest, I would definitely trust him.
Good luck with your pregnancy. I hope you have a happy and healthy nine months.