Please tell me, could a blood pregnancy test be wrong?

Yes, sort of: A blood or urine pregnancy test detects HCG hormone, not pregnancy per se. If a person has a tumor producing HCG the test will be positive but wrong in that the person is not pregnant. If you do the test too early and it is negative, it could be construed to be wrong as the women is pregnant but the fetus has not yet made enough hcg.