What is the point of having two weapons as a whirlwind barbarian?

I play as a Whirlwind-Barb. I'm currently using Grief (Phaseblade - WeaponSpeed: -30) on my main hand and Oath (Highland Blade - WeaponSpeed: 5) on my offhand. I am thinking to create another Grief in a Phaseblade. But I came across something really interesting on Diablo Wiki - Whirlwind:

Dual Wielding. The hit-check alternates between the weapons, producing an overall result of damage about equal to the average of the two weapons. If one weapon is slower, the frame rate will be adversely effected, so it's best to use two weapons with the same frame break (see below), or else just go with a single weapon.

This quote is very confusing and counter intuitive to me. Does this mean that a ww-barb with 1 grief phaseblade does as much damage as one with 2-grief phaseblades? Wouldn't it be great to use a good shield in the offhand if that is the case? In my current case: I should then remove the oath, because it does way less damage than the grief phaseblade. And my plan to create a second grief would be just a waste of a Lo-Rune? Can anyone confirm that?

Does this mean that a ww-barb with 1 grief phaseblade does as much damage as one with 2-grief phaseblades?

Yes - the damage comes from one weapon at a time. Since you are using the same base weapon with a runeword in it, the only difference between the weapons would be the percent roll you'd get on it.

Wouldn't it be great to use a good shield in the offhand if that is the case?

No, when you block there is an animation, when you are a WW Barb, you want to continuously move and heal through the incoming damage.

It would technically be a waste to add an additional grief, unless you REALLY want that +life and +mana on kill. All of the other stats on grief count when you hit an enemy.

Although expensive, and basically impossible in single player, top end gear WW barbs use a Breath of the Dying 2-H Mace.

I think the discription was wrong. The right mechanic is as follows:

When dual-wielding, both weapons try to score a hit against the target. In other words, the game does a hit-check for each weapon. Since both weapons are given the chance to score a hit, the damage done over time is roughly the sum of the damage of both weapons, which is comparable to the damage done whirling with a two-handed weapon. The effect of weapon speed in dual-wielding Whirlwind is as follows. While a target is in range, one of the weapons' speed is constantly used to calculate the next hit-check frame. If there's no target in range, the game will alternate between weapon speeds to calculate the next hit-check frame. The best way to make sure you have maximum Whirlwind speed when dual-wielding is to use weapons that both reach the final breakpoint, like for instance a Lightsabre phase blade and a colossus blade with 40% IAS.