I'm not saying you're wrong about how TOT saw it--I'm not him, after all--but I can say that I would feel the same way as him about someone from work being at a funeral or wake for one of my relatives, and not because I saw it as devious or disingenuous or anything like that. They just simply aren't a part of my life in that way. The last thing I would want to think about in that situation is work, and having people from work there (even though they had nothing but the best intentions) would not help me in any way.
(Yes, I do have a couple of friends at work about whom I would not feel this way. The difference is that they are "friends I work with" as opposed to "coworkers with whom I am friendly"--the category 99% of the team falls into.)