How does does statistical data about gun ownership help physicians "clean up the damage"?
It doesn't. The doctors do.
No dog in this fight on my part. The OP wanted to know why the doctor was asking, I linked to an article showing the kinds of data physicians are collecting, and offered some reasons why they might want to do that. If you disagree, take it up with them, not me.
What is kind of interesting here, though, is that this discussion does give us a moment to reflect on the other half of the equation. Most people here are fixated on several specific actions:
1. Identification of threat
2. Reaction to threat
3. Bringing weapon into play
4. Target acquisition
5. Deployment of weapon
And that's usually where it stops. Those who think a bit deeper on these matters give some thought to legal ramifications, lawsuits, lawyer fees, etc. Going a little further, we also have the problem of the person who has been shot (could be you, too). Somebody has to patch that person up, oversee their rehab, provide wound care, medication, possibly prosthetics and reconstructive surgery. This is rarely discussed.
But if we had any ER surgeons here who could weigh in, particularly those from an urban area, they'd probably tell us about Friday and Saturday nights when the gunshot wound victims turn up and how much trouble that is. We'd hear more about domestic shootings and self-inflicted wounds and so forth. Somebody has to pay for that care, and it's a burden on the healthcare industry. So you can kind of understand how they might want to get some understanding of the causes of these things and how the incidence of them might be reduced.
The key point here is that all of this is their business. It is reasonable that they would have concerns about this from an epidemiological perspective, just as they do with things like drug and alcohol and tobacco use.