Side line: “kata sarka” (according to the flesh) must be taken as adverbial, it qualifies verbs for “knowing” – how they know or in this sense not knowing – “not according to the flesh.”
The good people thought that if those two had found some satisfaction of the flesh between themselves, then it was a matter concerning them and God alone.
These are people who differ from ordinary people in the same way that the body differs from the soul. These are people who are meant to be ruled, and for them their nature is best realized if they're slaves.