Let's examine the evidence:
http://www.atlantishealthcare.com/outcomes
Oops we can't actually examine the evidence because they don't tell us the name of the study. There's also the question of whether improved adherence actually translates into better outcomes (maybe patients are better at finding the right dose than their doctors).
They also refer to other studies for other health problems but again no title is given.
My impression: information is presented selectively to readers for the purpose of persuading them, which suggests that readers would be less likely to persuaded if they were in possession of all relevant information.