[it]

I feel like I should explain better....

The leap of logic you are making is that "a test" does not have to be an actual concrete disqualifying test judging the person's qualifications and legally preventing them from running, but rather that people judging the qualification of the person fall under such a test.
The idea that personal judgement holds any weight at all, or it's current evolution to the notion that personal judgement is bad, is a rather modern one. The semantic framework did not exist at the time, and for someone to try to establish it would been nothing short of poetry (Or a day to day conversation in my 1st marriage).

In contrast, the established concept of such a test at the time was the one given by the heritage of a newly independent British colony, that no longer serves a Monarch that used to have a religious requirement for the sit.