I’d agree with your doctor friend because on a nice piece of meat like steak or a joint, any nasty stuff like E-coli and various other nasties are on the outside, which gets thoroughly cooked, the meat inside that is rare is well protected from all this, so safe.
If you then take that meat and mince it up, any contamination on the outside is now spread all the way through it, and left to fester and grow on the inside for days until used – that’s why it is imperative to cook it all the way through.
The reason why steak Tatar is still low(er) risk and OK to eat is because it’s cut and minced only a few minutes before serving, and does not get that nice chance for everything to fester away inside out of sight at ambient temperatures as tends to happen with mince.
Obviously, if you are cutting and mincing meat at home for rare burgers, then you are at much reduced risk (well, unless you are using unpasteurised eggs as a binding agent…)