What causes you to interpret it as "fear of scrutiny"?
There is no other explanation for keeping it secret, other than that they are afraid people will comment on it. The excuse given by Bishop Fellay is that the Pope is afraid of the "progressives" commenting on it. But since he won't even give the text to his own priests, and they seem to resist the agreement so far, it's pretty clear that there is a fear of scrutiny even by his fellow priests.
Catholic doctrine isn't a secret of the lodge, but it might as well be, if you accept the mysterious prating of neo-modernist theologians, I don't know who can fully understand it without some sort of training in the field.
You try to personalize this but the simple fact is that the teachings of Catholic doctrine concern everyone, they aren't a matter to keep secret, and those who say it's "none of the laity's" business what points of Catholic doctrine are being proposed and negotiated behind closed doors apparently don't understand the purpose of the SSPX, which isn't about coming to secret agreements behind closed doors with modernists.