I know that many people, doctors included, are trying to get rid of the blood screening test, at least as a general blanket test for every mother. The test can NOT tell you whether your baby has abnormalities or not, just if there is a chance. This test causes much unneeded panic and the stress caused on the mother can be worse than the risk of abnormaility itself. The only information the blood screening test will give is if more invasive testing is needed or not.
We had the blood screening test done, got back "not so nice" results, panicked for over a month while spending extra money and causing more risk to have other invasive tests done, only to find out everything was fine. Next time, I will opt out of the blood screening test, especially if the ultrasound tests all look good.
That being said, after all of the testing, now we KNOW 100% everything is fine and it has made the rest of the pregnancy wonderful. But, the only way to know for sure is by doing the more invasive testing, such as amniocentesis, which by the way, is much safer than originally thought!
Anyways, listen to your doctor. If he/she tells you everything looks good, listen!