Two facts about physical therapy patients, broken out by treatment length:

Short-term patients (less than six weeks): about 31% showed major improvement. This rate was the same for patients treated by a GP and patients treated by a specialist.

Long-term patients (six weeks or more): about 50% showed major improvement. Again, the rate was identical for GP patients and specialist patients.

It's worth pausing on the phrase "regardless of whether they were treated by a general practitioner or by a specialist." This doesn't mean "we didn't track who went where." It means the 31% and 50% figures each applied equally to both practitioner types. GP patients hit 31%, and specialist patients hit 31%. GP patients hit 50%, and specialist patients hit 50%.

These matching rates are the phenomenon. The author observes them and offers a hypothesis to explain them: since the rates are the same no matter which practitioner patients saw, the choice between a GP and a specialist must not affect your chances of major improvement.

The author treats the matching improvement rates as proof that the choice doesn't matter. But matching rates can be misleading if the groups being compared aren't similar.

Here's an analogy. Suppose 60% of brain surgery patients and 60% of podiatry patients show major improvement. Same rate. But you wouldn't conclude that it doesn't matter whether you see a brain surgeon or a foot doctor, because the patients going to each doctor have completely different problems. Send a brain injury patient to a foot doctor, and their recovery rate probably drops to near zero.

The same issue applies here. The patients seeing GPs might be a relevantly different from the patients seeing specialists. If they are, then matching overall rates don't tell us anything about whether the choice matters for a given patient.

In this scenario, both practitioners show 31% overall, but the GP is far more effective for Group X patients while the specialist is far more effective for Group Y patients. A Group Y patient who goes to a GP would have only a 10% chance of major improvement. The choice of practitioner would matter enormously for that patient, even though the aggregate numbers are identical.

The two time periods (short-term and long-term) are a bit of a distraction. They're included to reinforce that the rates match across both groups. But this doesn't fix the core problem. Even if the rates match across every time period, the choice could still matter if the patient populations seeing each practitioner differ in some systematic way.

We're looking for an answer that identifies something the argument fails to account for about the comparison between GP patients and specialist patients.