https://classic.7sage.com/lsat_explanations/lsat-23-section-1-game-2

I watched the explanation for this game and am struggling with why in the set up you can not assume that HIRED equals INTERVIEWED (i.e., that they are interchangeable terms), since interviewing is a required condition for hiring?

I interpreted the corresponding rules to be just attempting to confuse me and depicted all hires as, by default, interviewed in my rules interpretation, e.g., I interpreted rules 4 and 5 to be combined as: F-K-M (if F then K then M). But clearly this does not work in the execution of the game!!!

Why is this not a valid interpretation?