But it is. I run into chords on lead sheets all the time that say stuff like C13#11. Man do you know how many notes are in that chord? I'll tell you...there's 7 ..how many strings on a guitar? there's 6...so even at best (if you had the most elastic hands on the planet) you could only actually play 7 notes of that chord, and you have to pick one to omit. does that mean the chord isn't a C13#11? no, it just means you can't or chose not to play them all, doesn't lessen the chord.
It's all about function and what part the chord is playing in the grand scheme of things that really determines what the chord is. It's all about context. I play chords that can be called multiple things all the time. How about G7b9? I play that one regularly, I play a xx6767..which means I don't play a G in the chord at all! but it's still a G7b9..or it could be called a Bdim, or a Ddim, or an Fdim, or a G#dim......chords have multiple names, bottom line. It's all about context and what other musicians would be playing around it.
I don't buy the Fminb5 because that's not how the chord sounds like it functions in that series of chords, it's as plain as that. If you feel it does, then call it that if it makes you feel better about yourself. Personally, that's not what I would call it.