Thanks for the replies. As it turns out right after my post I closed Sketchup and LayOut again and reopened. That corrected the issue that I was having, which is strange because I had closed and reopened the apps a few times before and it did not help at all. I am not sure what the change was the last time. Although I do not know what the actual problem was, at least now everything seems to working as I expect in the way that I use Sketchup.
I see your point on the proper use of layers. I often wondered why entities within a group could be on a different layer than the group as a whole. I will definitely use that procedure on the next model.
Thanks again for the replies. It was definitely an "aha" moment after reading them.