The parts guy said the part is compatible because it's the same sprocket, does that sound about right?
That makes sense, if what you're saying is that he looked up sprockets for the two models and found that they used the same part numbers in his book. This would not be surprising to me, based on what I'm seeing in the respective Parts Lists:
K1,K2 23801-300-315 Sprocket, Drive (17T)
K1,K2 23801-300-000 Sprocket, Drive (16T)
K1,K2 23801-300-010 Sprocket, Drive (17T)
K1,K2 23801-300-620 Sprocket, Drive (18T)
K4,K5 23801-300-620 Sprocket, Drive (18T)
F,F1 23801-300-010 Sproket, Drive (17T)
So the F and F1 take the exact same part number for the front sprocket that came stock on some early K machines.
So given the question "Are K series front sprockets compatible with F machines?" the answer seems to be yes, at least as far as fitting on the shaft is concerned.
mystic_1