Usually many names are given to the Bishop or Area Authority and they conduct multiple interviews for them. Then the individual conducting the interview goes with who they feel prompted to extend the call to, which would result in a separate interview and a formal call to serve. In fact, they get very personal about their financial and legal obligations, this pre-calling interview allows them to remove some from consideration so they’re only taking qualified people to the Lord.
So yes, while what Brisco said sounds like a KWhitt move it’s actually pretty standard operation. Like you said thoigh, if the circumstances don’t allow then an individual would not be wrong to decline but that’s why they conduct the prelim interviews. To allow the individual time to really consider the ramifications of accepting the calling.
I get it, the process sounds more like a business and less direct inspiration but its a pretty important calling so they only take prepared individuals to the Lord. Of course, He can throw it back at them and call somebody else but this is the general process followed for those callings.