Jefferson, Lincoln and Theo Roosevelt never HEARD of the 20th Amendment. It was ratified in 1933, long after the aforementioned had gone to their eternal rewards.
That leaves (from your examples) Eisenhower and Reagan, both of whose life stories and family histories were well known as opposed to, say, someone about whom absolutely nothing is known or verifiable. So that’s a pretty lame counter to the question raised.
So that’s a pretty lame counter to the question raised.
No, it's not.
The requirement to be a natural born citizen is 200+ years old. The 20th Amendment is irrelevant, which was the point of my reply. The standard was the same for Thomas Jefferson as it was for William Jefferson Clinton.
"Well know life stories" is not a legal threshold. It doesn't mean anything, other than "the people will decide". Other presidents weren't required to submit paperwork to prove where they were born.
If it's the realm of public opinion to do the vetting, then ... it's the realm of public opinion to do the vetting. Which is exactly what happened.