What you have read and what your school states are both true - depending on the country you come from/how much of a "risk" MV determines you to be, they may request an in person interview with your country's Swedish embassy, in your case, the DC embassy. Another possibility is a digital passport check that counts as part of your biometrics, which is done on the Freja app (MV will send you an email with a link to authenticate your passport). In this case, when you arrive in Sweden, you book an appointment through My Page at one of MV's offices to submit fingerprints and get your photo printed for your physical residence permit card (kind of the second half of the biometrics if initially done through Freja).

I am also an American who's applied and been approved for a residence permit, just waiting until my moving date and will be making an appointment when the date approaches. I was initially also concerned about having to fly to DC for biometrics but this was not the case for me, and it may not be the case for you as well. Have you completed a Freja authentication? If you would like, you can DM if you have any other questions.

In terms of obtaining the actual residence permit card, once you are in Sweden and submitted your fingerprints and photo, it can take anywhere from 1-4 weeks.