Rigorous testing is all well and good, but we do know how many errors crop up in scientific papers, right? A lot.
The gold standard of testing is double-blind, randomized, placebo controlled studies and this is only done sometimes for vaccines, as far as I aware.
I believe there are certain circumstances such as no safe and effective already existing vaccine, or where there's a certain kind of benefit to the injected population, where vaccines are generally allowed to go through this double-blind, randomized, placebo controlled studies (the gold standard of testing) and certain circumstances where they do not go through such rigorous testing.
I believe this ethic stems from Jonas Salk's decision during the development of the Polio vaccine where the ethical call was made to not do double-blind, placebo controlled testing due to the desire to prevent damage to human lives that could be prevented by not using a placebo.
I invite fact-checking on everything stated.