It was never proven at the time that he did not qualify, but apparently he didn’t qualify (at least, after the fact some say that and say it’s proven). So, it’s possible that Obama may never be proven to not qualify — and maybe “after the fact” (after he’s left office, it may be proven..., who knows...).
The thing that is at issue is that the allegations are not proven (first item) and then (second item) a person takes the office of President (under those continuing allegations of not being qualified [but not proven]).
It sort of sounds like what may be happening with Obama is what happened with President Arthur.
The allegations (for President Arthur) are that he was born in Canada (and now someone else says that there were questions of being born elsewhere, other than Canada, outside of the U.S.). So, there were multiple allegations, apparently.
You seem to intentionally concentrate on what suits you in comparing the Arthur case to the Obama case. There are a vast amount of differences involving these two cases.