The problem is that it does not define what constitutes the power rating of the xfmr.That article is obviously made for resistive loading only, and is correct in that context IMO.
Let's take a simple example, of a xfmr with two identical secondaries. The xfmr is rated at 100VA.
The article (and many others) considers that each winding is capable of 50VA. What happens when one secondary is unloaded and the other sees a load that draws 100VA? Unless the wire gauge has been made dangerously small, this loaded secondary will deliver a large percentage of the nominal VA rating. That is because flux circulates in both secondaries and flux is governed by the primary (and the core) alone.
In a center-tap configuration, each half secondary is instantly capable of delivering the whole power rating. In teh name of energy conservation, it can only do so half the time.
This situation may or may not be sustainable, depending on the safety factor the winder has taken. Note that this safety factor is not decided by the possibility of overload alone; actually it is the result of minimizing DCR.
I agree with the fact that the rms currents are smaller for the bridge configuration. However, paralleling two secondaries exposes to the risk of losses due to voltage unbalance.