Its about common sense, a stronger person will hit harder than a weaker person. A perkier person will do the same? No. Fact is:
Attributes,skills and perks>just perks and skill.
You are working under the fallacy that there is only one way a person can be physically "Strong"... I prefer the term "Conditioning"
Perks, if anything represent actual expertise in that area, while skill is more like the conditioning to use it.
Some people are built to bear heavy loads, but lack the body mechanics to hit hard. Others can hit hard with one hand, but are too uncoordinated to hit hard a weapon held in both hands (or vice versa). Others have strong limbs capable of dealing punishing blows, but lack the structure to support heavy loads. I know I can lift
very heavy loads, but hit like an Airzooka.
However, Skill represents physical conditioning to accomplish the task as much or more than it does raw expertise. And the discrepancy between high skill in one of the two combat styles and low skill in the other can be excused as loss due to inefficiency of using the style.
Someone who has high skill in both One and Two-handed combat can be assumed to be physically stronger than someone with low skill in either, but his encumbrance might be the same because he's conditioned his strength in his arms so he can hit harder, not his back and legs, to carry more junk.
Likewise, someone may have low weapon skills, but have a great encumberance... he can be assumed to have a strong back, but weaker arms.
Skill, from a gameplay stance, represents conditioning as much as it does expertise. Skyrim's more about the end-result when it comes to skills, perks, and attributes, not the little things that add up. You can fill in the blanks yourself.
Mathematically, they used to have Weapon Skill = X, and Attribute = Y. Now we have P=Perk Bonuses
Damage = X + Y. That calculation is constant between Oblivion and Skyrim, as well as Skyrim acquiring the formula:
Damage = S+P
Except, now, Weapon Style = S
S=X+Y-P, where P = Damage - S.
It all ends up being a very, very convoluted way of saying "You can decide how much of your character's demonstrated damage-dealing ability comes from physical fitness, and how much comes from weapon expertise. We don't really care, because you're still hitting just as hard either way"