The silence perk only effects movement sound. If they see you, you're still in trouble. Also, you have to be sneaking to not be seen; otherwise, you're not actively disguising your movement. Even when you're sneaking, there's run and walk modes; this is what the perk refers to.

Here's my equipment:

Glass Helmet (Flawless). 60 AC. +40 Lockpicking. +25 Illusion
Necklace. 0 AC. +40 Sneak. +40 One Handed
Glass Armor (Flawless). 136 AC. +25 Light Armor. +62 Magic Regen
Glass Gauntlets (Flawless). 48 AC. +40 Sneak. +40 One Handed
Ring. 0 AC. +40 Sneak. +40 One Handed
Glass Boots (Flawless). 48 AC. +40 Sneak. +1? Muffle

Glass Shield (Flawless). 56 AC. +20 Magic Resist. +37 Shock Resist.
Dragonbane (Legendary). 120 Dmg.

Ebony Dagger (Flawless). 41 Dmg.

Including the sign of The Lord and natural resists, I have 398 AC (above the armor cap) and 70% magic resist