In reviewing this article, I couldn't help but notice the problems in how this information was reported, so that it became quite apparent why the general public perpetually misunderstands or misinterprets evolution.

"Our results demonstrate, for the first time, that Coal Forest fragmentation influenced profoundly the ecology and evolution of terrestrial fauna in tropical Euramerica, and illustrate the tight coupling that existed between vegetation, climate, and trophic webs." (Abstract)

"Specifically we test the hypothesis that population constriction into isolated rainforest islands exerted a major impact on tetrapod diversity, ecology, and the development of endemism. In doing so, we draw on the theory of island biogeography (MacArthur and Wilson,1967), which was developed to explain patterns of diversification in oceanic islands, but is equally applicable to other kinds of islands, e.g.,rainforest refugia."(1)

So effectively we have a paper that indicates that the fragmentation of the rainforests into "islands" created the kind of diversity and endemism as predicted by the theory of island biogeography and is even referenced in the article as a "classic ecological response".  So what happened when this got translated for the public?

"Global warming devastated tropical rainforests 300 million years ago."
While the original paper states "In cratonic areas of North America (where the effects of tectonics can be excluded), an abrupt shift to more arid climates has been linked to rainforest collapse (DiMichele et al., 2009, 2010), though the exact causal mechanism remains uncertain. One hypothesis is that aridification was triggered by a short-term but intense glacial phase."

So it begins with the reporter clearly taking liberties with a particular perspective which is intended to foster a particular agenda.
"Now scientists report the unexpected discovery that this event triggered an evolutionary burst among reptiles -- and inadvertently paved the way for the rise of dinosaurs, 100 million years later."
What's interesting in this quote is the use of the word "inadvertently" as if evolution proceeds with intent or purpose under normal circumstances, but it completely missed the collapse of the rainforest so there was some unusual twist in what came next.  There is nothing intentional about evolution, so in one way, everything that occurs is "inadvertent". However, while I realize that this usage originated with the reporter, it is a clear indication of the kind of sloppy scientific journalism which is such a problem.  I'm also not clear on what precisely was "unexpected" in this paper.  
"But when the Earth's climate became hotter and drier, rainforests collapsed, triggering reptile evolution."
Once again, the problem is that it suggests that evolution occurs with a purpose and that it is normally dormant until some event "triggers" it.  At this point the reporter has reversed causation by indicating that it was the hotter, drier climate which gave rise to the rainforest collapse, instead of reporting as indicated earlier that the rainforest collapse (cause still uncertain) is what gave rise to increased aridification.

However, even the original authors aren't exempt for embellishing the results in directions not demonstrated by the study.
Ms Sarda Sahney, also of the University of Bristol, UK said: "It is fascinating that even in the face of devastating ecosystem-collapse, animals may continue to diversify through the creation of endemic populations." However, she warned that: "Life may not be so lucky again in the future, should the Amazon rainforest collapse."
I can't even begin to imagine what she was thinking when she said this.  Of course, diversity tends to increase when environments change, since this provides the greatest opportunity for natural selection to operate.  The more new niches open up, the greater the opportunity for modifications to find a place to thrive.  This is hardly unexpected, although it is equally not assured.  However, the statement about the Amazon rainforest is truly baffling.  Are we to believe that life on Earth is threatened by the collapse of the Amazon?  Surely she can't be that naive.  This is the kind of propagandist nonsense that turns legitimate scientific inquiry into political agendas.  Life is certainly not in jeopardy, regardless of what happens to the rainforest.  Certainly HUMAN life might have problems, but life on Earth is not the issue.  To suggest otherwise is making a claim with no scientific backing.
"They showed that reptiles became more diverse and even changed their diet as they struggled to adapt to rapidly changing climate and environment."
In this final statement of the article it once again suggests that evolution (or natural selection) operates with a purpose, as if a species "struggles" to find its proper adaptation for the new circumstances.  This kind of verbage simply promotes a general misunderstanding of evolution and natural selection and is a disservice to serious scientific inquiry.  When this is linked to the popular mythology that only random mutations can initiate changes, it's little wonder that most people find this type of "science" hard to believe.

(1) Rainforest collapse triggered Carboniferous tetrapod diversification in Euramerica
Sarda Sahney, Michael J. Benton and Howard J. Falcon-Lang