I understand your point - and it's well taken. But the proof is in the pudding so to speak. Ideally these situations should be treated on a case-by-case basis. Using two Shenandoah NP streams as specific examples, the increase in percentage of browns in the total fish population (brook trout, brown trout) has had a quantifiable negative impact on numbers of brook trout. In this case, the NPS has initiated shocking the browns out to at least control their populations, such that the browns that are removed are relocated to delayed harvest streams and other waters that do not support brookies. I actually favor this approach over the killing of browns outright - they're effectively recycled into at least one Valley spring creek and can hold over in another which has a DH section.
On the other hand, one of the waterways that border the Shenandoah NP has coexisting brookies and browns, with the browns having gained a foothold after a single stocking event in the 1960s. Anecdotally the brook trout numbers are lower than before introduction of the brown trout, but they're certainly still there and reproducing - probably maintaining some sort of brown trout/brook trout equilibrium after so many years.
The problem with the stream mentioned in the article and at the beginning of this thread is that due to low water conditions for several consecutive summers, the native fish have been descending downstream to find flows that are still within a suitable temperature range and therefore oxygen supply. The brown trout are found primarily in those same lower reaches, so the brookies are a brown trout chow of sorts. They never had to compete with other piscivorous fish historically within the parts of stream that can sustain brookies. Drought summers are not a new challenge to these fish. Hungry fish-eating brown trout are. In this case, I'm not so sure leaving the browns to threaten natives is a good idea.
As to the sentiment about introducing trout into ditches that were completely or nearly depleted of fish due to environmental issues - as long as they're not displacing a threatened species, not an issue. Creating a fishery out of a non-fishery is a great idea, but supplanting one with another seems asinine to me.