Both the premise and conclusion concern major improvement. The author does not reason from a premise that establishes there’s no difference in effectiveness and bringing about “any” improvement.

Difference between short-term vs. long-term injuries doesn’t matter; we already know that among short-term patients, GP and sp. have the same major improvement rate; the same applies for long-term patients. What matters is whether GP and sp. treat different kinds of injuries.

The statistics are based on a review of records and what they show about major improvement. Whether patients are more likely to “report favorably” about one type compared to another doesn’t matter, because this bias doesn’t affect the records of improvement.

We already know the % who saw major improvement for each kind of therapist. The number of patients doesn’t affect the % of patients who saw major improvement.

If GPs and spec. excel at treating different kinds of injury, then if you have an injury that spec. excel at treating, your chances of improvement are higher by going with a spec. The opposite applies if you have an injury that GPs excel at treating.