That’s a complicated one that would take a long time to cover fully. It turns out not to be true, quite. Traditionally, turtles were thought to be “anapsids”, primitive compared to other reptiles and an isolated group. Their morphology is so modified that it was hard to place them well. But back in 1994, Olivier Rieppel did the first rigorous phylogenetic analysis and figured out that they were actually diapsids. Hedges et al. (the paper referenced in your story) analyzed a short sequence of DNA and got an ambiguous result, but it put turtles also within diapsids and for the first time in the neighborhood of archosaurs. More recent, larger analyses have all converged on turtles being the sister group of living archosaurs, i.e. of birds and crocodylians. So what we have here, in contrast to your claim, is increasing consilience resulting from better data.
That’s a misleading headline; it’s really just talking about Pegasoferae. It might be correct. But I don’t see any major contradictions there.
Actually, quite close, though not perfect. Some parts of the tree are easy, others are hard. Longish, fairly recent branches are easy. Short, ancient branches can be difficult. Due to incomplete lineage sorting, some genes actually have slightly different histories than others. Some sequences aren’t long enough to resolve short branches. Inadequate evolutionary models may cause other problems. Nevertheless, the data have a clear structure, much more than expected from anything other than phylogeny.
Hedges S.B., Poling L.L. A molecular phylogeny of reptiles. Science 1999; 283:998-1001.
Rieppel O. Osteology of Simosaurus gaillardoti and the Relationships of Stem-Group Sauropterygia. Fieldiana: Geology New Series 1994; 28:1-85.