You asked — “So, in other words .. it’s possible the system failed due to the purposeful deceit of the candidate and negligence of the respective officials, and the American people were duped.”
Very true, it’s entirely possible. But, no one could *prove it* and that was the same problem they had back then, too.
So, taking a “lesson from history” — what kinds of problems did Arthur have with signing legislation? Any? Did a law enforcement/sheriff/marshall try to escort him out of the Presidential office? Did the Supreme Court try to remove him? Was there an impeachment of him? Did other foreign governments blackmail him? Was the Constitutional requirement for office *forever altered* never to be respected again?
History will provide you that answer...
Of course not, since, and read slowly, IT WAS NEVER PROVED.
All the things you list would have been a problem, if the issue were proved, and will be IF it comes out that Obama is not eligible. IF it never does, then obviously it won't be a problem with him either. But that's a big if these days. Is there any evidence that once Arther was elected VP, and became President via an assassination, there was any serious effort to uncover the truth. Also consider that there was not nearly the paper trail in those days as there is today. Plus no electronic records, no internet, etc.