> Sure it does. The death or major illness of a sitting president is impactful in a way that the death of an average retiree is not.
The recommendation is not based around the public impact of the patient's death, but around the expected utility of the test in improving the length and/or quality of the patient's life, which is fairly low in the best of times for PSA screening.
A president and their team is absolutely going to take a "better safe than sorry" approach. The doctor is not the only person who decides what treatment should be, the patient does too.
PSA is not fool proof test, and is susceptible to false positives. A substantial fraction of men, in the 40+% range have prostate cancer at death. The treatments for it can be painful and have long recoveries, so there's not obvious solutions.
The recommendation is not based around the public impact of the patient's death, but around the expected utility of the test in improving the length and/or quality of the patient's life, which is fairly low in the best of times for PSA screening.