Would you suddenly stop and disengage if the person in front of you disappeared, when you're aware of the ability to cast invisibility?
No, you'd probably stay alert and track him, especially if he's being a noisy pile of noise while invisible.
Herp derp.
Muffle silences your armor so that you can sneak more effectively. Just look at the description of the spell: "You move more quietly for ___ seconds." More quietly does not mean completely silent, and if you're just walking through, they will hear you and track your position based on the noise you're making.
Cast muffle, go into sneak mode, and cast invisibility. You will be much more likely to pass through the same situation without being detected.
If you had been paying attention...you would have seen that I addressed that. The GAME contradicts itself where the Illusion skill is concerned. It says it's one thing, then acts like it's another.
Muffle DOES NOT mention armor creaking or sword clanging in any way. Just says you are "quieter". Not why you are quieter. The Illusion trainer says it's mind magic. Muffle should be moved to Alteration, or the description made more clear.
And, YES, you would disengage if someone vanished, and moved. Because you are unable to perceive them no...sound...wind...leaves/dust disturbed. Nothing. Just exactly the way it was in Oblivion. You aren't telling his mind that he can't see you. You're telling his mind that you aren't there.
Stated in many places that Illusion is mental. And that is how it works, if it IS mental (altering the mind...not matter)