Don't dispute your math - just your logic.
Extremes might make it more obvious:
Imagine administering a procedure on 8 billion human beings (the pop. of the planet).
An indefinite number of White people die (in this example, we aren't interested in their fates).
Of the Black people, one hundred die.
Sixty of the Black people died under the care of a White physician, the other 40 under the care of a Black physician (we assume that the differing number of Black vs. White physicians has been controlled for - in our example, we can pretend that there were an equal no. of Black and White physicians).
Wouldn't you be extremely curious about the differing mortalities (disaggregated by race)?
Or would you really simply "divide by the total rate of survival?" After all, literally billions survived the procedure!
Again, don't want to "lock horns" with you. But I sincerely believe that, after a little reflection, you'll agree with me.
I maintain that the observed difference in the real-world study is probably attributable to OTHER FACTORS (incl. small sample size, as you point out).
Regards,