Arbiter of Wyrms said:
If the designers' intent is that dwarven barbarians should move faster than human tanks, they have not been sufficiently explicit about it.
That is one thing I know for sure I can agree on.
The problem lies in the SRD quote's use of the pronoun "this speed." The pronoun follows a separate sentence which states "Dwarven base land speed is 20 feet." That sentence is two noun phrases "Dwarven base land speed" and "20 feet" joined by "is", making them equivalent. So, humans resolving the "this speed" pronoun don't even worry about whether it refers to "20 ft" or "dwarven base land speed," because it doesn't matter.
However, in the case of dwarven barbarians, the base speed is no longer 20 ft, it becomes 30, thus the first sentence is invalidated. That leaves the reader to try to determine what the designer meant when they said "this speed." Both noun phrases are speeds, so there's no easy answer there. So, the reader falls back on their biases and intuitions - that's why one reading seems obvious to some, while a different reading seems obvious to others.
"20 feet"s proximity to the pronoun supports the "dwarves move at least 20 feet in medium armor" argument.
The parentheses support the "dwarves move their base speed in medium armor" argument.
Either way, we have no way of knowing, so I would say go with what suits your game best. Note, none of this has anything to do with the case where they're wearing heavy armor, where I think we all agree that the Barbarian speed bonus just goes away, and the speed is 20ft.