[puffoflogic]

How can their being prescribed treatment retroactively ruin the data point that they got sick in the first place?

And moreover, unless trials are just standing by and watching patients die, the fact that a patient received X intervention and lived (or X and died) is the only kind of data trials of prophylactics can collect anyways. It doesn't really matter whether the treatment is administered by the trial since the treatment is not being studied.

[refurb]

Because interventions beyond those being tested are closely monitored. Many are excluded, diagnoses need to be confirmed by specific tests, certain treatments may be required to stay in the trial.

Trials usually run for a set period of time. If a patient gets outside treatment half way through, all data beyond that point (including the final analysis) is tainted. So likely the patient would be disqualified from the study and all their data discarded (and they would just show up as "n=1 patient withdrawn from study due to outside treatment for X").

A good example is an eczema trial. Patient gets drug and is monitored for 1 year. If that patient goes to an outside doctor because the rash got worse and gets a steroid cream, and get better, now you don't know - did the experimental drug help? or the steroid? or both? Was the rash actually worse? Or did the patient just think so? The treating doctor never saw the rash prior, so has no baseline. And they likely didn't score the severity of the rash so another data point could be captured.

It's all very standard a part of controlling variables in a trial.