Nope. Skill determines armor rating. Even improved Elven Armor is inferior in AR to Dwarven Armor (Which has a much higher "Base" armor rating than Elven), especially as it's likely she has 1-3 "Juggernaut" perks. Not even Glass armor is better than Dwarven for her.
Truth. You have to take into account everything that goes to the armor calculation. Perks in the Heavy tree, perks in the Light tree, and the skill level.
ALSO:
Your level actually plays a part in this. Remember, Lydia doesn't level up (presently) so her skill level is going to be whatever it was when you first met her. So if you met her at a low level, she won't have very high skills or perks, so it's easier to get her to switch (until you use the console to update her level).
But if you met her at a high level, then she has lots of perk points and probably spent them on heavy armor.