Bit of thread drift here. There will always be situations outside the scope of the QRH. The QRH acknowledges that, and in those situations procedures should be varied as necessary for the best safety outcome.
But that's not the discussion here. An engine fire warning is not outside the scope of the QRH. So, the question is whether to interrupt an engine fire checklist and start testing fire loops (without the other pilot punching you on the nose). I recommend that you don't. So does Boeing - in the QRH introduction that apparently I haven't read. Don't make **** up. And, no, you are not going to put a B737 in a grass paddock just because an engine continues to burn. It's not an F27.
Where it might go outside the scope of the QRH is if there are other simultaneous problems perhaps caused by an engine shredding itself - such as a jammed aileron, hydraulic leak, depressurisation, gear problem, etc. This is where you get to decide on the most appropriate course of action, or priorities of action, using all that experience and airmanship that apparently I don't possess.