That is very true.

As for the bit about Mulgrew, no. She did lend her narration to a 'documentary' that promoted Geocentrism but so did Lawrence Krauss, renowned physicist. Both regretted it. Kate said on Facebook:

I understand there has been some controversy about my participation in a documentary called THE PRINCIPLE. Let me assure everyone that I completely agree with the eminent physicist Lawrence Krauss, who was himself misrepresented in the film, and who has written a succinct rebuttal in SLATE. I am not a geocentrist, nor am I in any way a proponent of geocentrism. More importantly, I do not subscribe to anything Robert Sungenis has written regarding science and history and, had I known of his involvement, would most certainly have avoided this documentary. I was a voice for hire, and a misinformed one, at that. I apologize for any confusion that my voice on this trailer may have caused.

This is the Slate article she's referencing.