The Lab technician said there is no such thing as a false negative blood test result (Pregnancy)

How likely is it for a blood test to give a false negative? 

I just got a blood test done for pregnancy today. (Tomorrow will be 6 weeks since I last had sex). I then got what I assume was a period on my placebo pills, exactly three weeks after I last had sex on- it lasted 5 days (I have 7 placebo pills). I took pregnancy tests two weeks after period ended because my boobs grew after I got my period so that made me concerned. The urine tests were negatives 

So today would be getting my blood taken 1 days shy of 3 weeks since the period I got after sex and 1 day shy of 6 weeks since sex. 

Did I wait long enough to get my blood taken for pregnancy or did I possibly test too early for the hormone to be found in the blood?

 I asked the lab technician if it was possible that if this test came out negative that it could be because I took the blood test too soon? She said, there is no such thing as a false negative when it comes to blood tests. That if I get a negative blood test - then it's negative for sure. Then I told her how i read about women getting a blood test for pregnancy and it was negative then they went back a few weeks later, and it was positive, and she said that's because they had conceived between the time of their first blood test and second blood test.' id there is no such thing as a false negative blood test result, is she right?