If I may add to this discussion to provide OP with some direction:
To learn the basics on how to critique a research paper, you may want to start by reading this: https://www.ucalgary.ca/ssc/files/ssc/wss_critique_2014.pdf
I don’t mean to speak for Austin or Jordan but seeing as my views align nicely with theirs I can say with relative certainty that no one is saying that manual therapy doesn’t help a person feel better, the question comes down to the mechanism of action of the therapy and why resistance exercise is preferred over various forms of manual therapy, like ART, for more long-term benefits (i.e. pain relief, increased range of motion, soft tissue therapy etc).
Proponents of ART (I once was an ART provider myself and believed this narrative as this is what was taught in the seminars) would have you believe that they are manually effecting structural change to soft tissue as described in the ART patent: https://www.google.ca/patents/US6283916
We know this is not possible because it would require a tremendous amount of force to do so: http://jaoa.org/article.aspx?articleid=2093620
This review succinctly explains why ART or other manual therapies can never truly be evidence based: http://rfkidd.com/myofascial-release-kidd.pdf
This doesn’t mean that manual therapy, lending to a placebo effect in the absence of a concrete mechanism of action, is not effective in short-term pain relief or short-term increased flexibility/range of motion. It can be effective, just not for the reasons that most people believe (i.e. no bony realignment or soft tissue structural change is actually occurring). The onus here lies in the narrative that a manual therapy provider supplies to his/her patients. A provider can be honest with his/her patients and explain that the mechanism of the therapy employed is not well understood and can still provide symptomatic relief of a person’s complaints, resulting in positive outcomes http://media.virbcdn.com/files/e2/967964ac72409a85-CarvalhoPAIN2016.pdf.
But it is also equally important for a provider to inform his/her patients that exercise in the form of resistance training is a powerful intervention, with well understood mechanisms of action, that can effectively confer actual structural soft tissue change for more sustained physical attributes/benefits, in the case of this discussion; range of motion.
I will make one caveat: this recommendation against pursuing additional dedicated time and resources to stretching or manual therapy treatments is meant for members of the general population. For people who rely on or require greater than average range of motion for specific activities (i.e. gymnasts, ballet dancers, hockey goalies, MMA fighters etc.), I would argue that regular stretching is mandated for successful participation in such activities as it serves as practice for the movements to be performed.
I hope this may clear up some confusion.