As I recall there was a supposed plot for Black Sisters to help Taim escape and make him a terror on the world ... given that there would be a 100% chance of a Red in any group of Sisters sent after a FD and the fact that a much larger proportion of Reds are Blacks and that the woman likely to pick the Red who would lead the expedition was Black (Galina) it's pretty easy to conclude that some Reds have been involved with raising FD in the past.

However, I do not imply that Logain was in anyway supported by the Red (or the Black) ... just that it's possible that in the history of the Tower that other FDs had in fact been set up by Reds.

The point is that it's possible Reds like Pevaara give this no credence because she finds it abhorrent, and in true AS fashion assumes if she believes it to be false that it MUST be false.

But what about Katerine Alruddin? She'd do it in a second. Run of the mill Reds aren't blind either, it's possible that some few suspect a woman like Katerine would not be above this action and thus are keeping their mouths shut because they know that there are more than a few women of their Ajah who could have been part of such a plot, and any of the Blacks in the Red would realize it could be a BA plot.

I'm not making wild guesses, merely offering a plausible (IMO) rationale for some Reds to keep their mouths shut on the matter.