Thoughts about The Cat Who Walks Through Walls

I've been re-reading the Robert Heinlein book The Cat Who Could Walk Through Walls recently and came to a revelation. (If you haven't read it, are in the middle of it or hate spoilers please read another post).

In Book one Richard and Gwen are run out of Golden Rule by the Manager and framed for the murder of Ron Toliver, but were they? Is it possible that perhaps the people that killed Toliver were actually Richard and Gwen on a journey from another time line as they are later in the book trying to save the sentient computer in Luna?

That is a WAY cool book. So glad to be re-reading it.