It isn't a good point. This was explicitly controlled for in the study. People are just making wild guesses about methodological limitations that don't exist.
>The effect size of surgeons’ birthday observed in our analysis (1.3 percentage point increase or a 23% increase in mortality), though substantial, is comparable to the impact of other events, including holidays (eg, Christmas and New Year) and weekends, which have been argued to affect the quality of patient care.