They did cut corners, though. Remember when the FDA was given a court order early last year (I think) to release all documents regarding Pfizer's covid mRna vaccine trials, and they finally agreed to release them but they said they'd do it over a 7 year period? And the first ones they released had redactions all over them, remember? So they were ordered to remove the redactions, and in the unredacted documents it was clear Pfizer cut many corners. Moreover, the trials were really sloppy; poor record-keeping, reported serious side effects were ignored, they were generally disorganized and actually violated certain protocol, including revealing the identification of participants and other information that's not supposed to be accessible in blind studies. (you can find info abt this online)
As for the vaccine rushed through during Roosevelt's presidency, he called for a traditional vaccine, a tried and very successful method which uses a dead or weakened virus or part of a dead or weakened virus and introduces it into people's bodies so their bodies can make anti-bodies against that particular virus. The thing that was new at the time is that that particular virus hadn't yet been tested. But researchers and experts were reasonably certain at the time that all viruses and everybody's immune systems behave in the same way, or at least very similarly. And they were right.