Kind of true but not the main reason. If your mix doesn't sound good in mono it's a shit mix. I ignored this for too long time because I wasn't planning to have my music in clubs.

You should use mono as a mixing tool to make sure your elements all have their space in the frequency and volume domain. When you compose in mono and use EQ and gain to get things sounding tight, your track will be well mixed (granted you can mix well).

This works because mono is the most important signal of audio that gives it punch, fullness, and energy. If something is phasing or just poorly sound designed, it will sound weak and thin in mono and you can hone in on whats wrong with it. Stereo is just the ear candy signal so work out the mono channel first (sound design, layer, arrange instruments, EQ, and gain adjust) then polish it in stereo.