Language Point 5

They understood instinctively that integrity involves having a personal standard of morality and boundaries that do not sell out to convenience and that is not relative to the situation at hand. (Para. 2)

Meaning: They knew by instinct that being honest means that one should have his own personal standard of right or wrong and know his limits, and that the personal standard should not be let down for ease or comfort, or altered by the present situation.

Please notice that both the second and third that-clause, that is, "that does not ..." and "that is not ..." modify the word "standard".