The thing is, a lot of things in general can be extremely easy to falsify but it isn't falsified because people aren't dumb enough to go through that many years of schooling and risk their professional license and career to falsify it. Like, the only paper trail when the nurses hand you medication at the hospital is their documentation, which they can also falsify while flushing your real meds down the toilet and giving you a placebo or other medication. Someone else might have seen it, or maybe the evidence is uncovered if some other medication shows up in your system, etc. which is all more likely the more times the same scenario happens. I mean, there are nurses who have murdered patients and were finally caught after a string of suspicious deaths.

If a pharmacist really decided to start doing fake vaccinations, eventually something can come to light.