Since farma is the presumed heir of the family, and he administered the correct treatment, it is viewed the same, as if his father had been the one to do it. Also, itd be kinda upsetting to the nobles if they knew farma cured it and she said "yeah i know you cured it, but sorry, gotta chop off your dad's head because he wasn't the one to do it, even though there were 30 other doctors here as well".