Yep, person doesn’t need to be in the US to receive the FBI check , I assume the issue here is that one of the spouses is in the US with pending asylum case and not able to travel ,more of a problem is to receive police clearance from your native country through the consulate (my friend is from India , they refused to issue him any assistance since he had no valid visa , so he had to give power of attorney to his parents , so they could get certificate from India for him and send it here). But that’s may be different from case to case . As of finger prints : VAC can be an option I guess ! In my case there was no a single VAC available around (only in NY) , had to go to USCIS visa supporting center .
In any case most of the possible issues are not critical and could be solved .