Erin, That "threshold" varies according to other complicating factors. MG is definitely one of those factors.
When I had hemorrhaged for months after a bad uterine biopsy, my hemoglobin was in the 8s after surgery. I had a transfusion (2 liters)! MG makes breathing worse, and anemia only adds to that. A savvy doctor will make sure that you have enough red blood cells in your body.
I just hope they have determined the correct cause of the low hemoglobin. An alternative to a sleep study is an overnight oximetry. You get hooked up during an appt. and then your O2 is monitored overnight. Very useful. I've had it done. A pulmonologist is normally who does that.
I really hope you can have that 2nd opinion! You need to stand up for yourself. Protocols can be changed. They often have more to do with a bottom line or a doctor's rating system than a patient's health. Sad yet true!

Annie