The light side also denies inter-personal relationships, meaning that its trust based on a paper history rather than deep history.
That's not actually true. The Jedi order denies interpersonal relationships, the light side simply requires that you don't give into your passions -- which is harder but not impossible
when you have strong personal ties. So it's a risk factor but not directly tied into light or dark. The council has simply taken that route as a precaution because they deal with a large group of people and know that a lot of their charges would fail to keep their balance if they allowed deep personal connections to flourish.