Hmm. Can't say I understand how your doctor's office thinks the various pieces of information here are compatible. And grr do I hate it when they prematurely assume that things are over when a mother's instinct says there is still something there. I had a doctor tell me I was having a chemical, and he said to go home and have a hot bath and a glass of wine, he'd see me next cycle. My "chemical" was born 9 months after that appointment, 8lbs 11oz.
I don't see how a line like that (and continued BFPs on a FRER) could have a beta of 1.2. Maybe the doctor's office printer put a "." between the 1 and 2 instead of after the 2, or maybe a member of the medical staff transcribed it wrong? Or like you said, a test mix up? Getting a negative qualitative test at the doctor's office after a positive FRER at home... sure, that has happened to me. (Dr. office tests just are not as sensitive as FRERs, in my experience.) But getting a beta of 1.2 with a faint pink line on a FRER of all tests...I don't know how the medical staff could not find that weird and at least try to come up with an explanation for it. I've heard FRER sensitivity goes down to 6 mIU/mL-10 mIU/mL.
The test lines look real to me. I see pigment, and I don't even have to squint.
How much darker are the current BFPs you're getting (compared to the tests you showed)?