Thanks for the scans. They look great.
I'm still not sure about James William's father's name being Thomas. I know for a fact that James Willis lied about his name on some of the census reports. He had issues with the law over the years (he was sued by members of his own family, assault charges were filed, he served time in jail).
Under normal circumstances, I would take the info in the funeral book to be correct. But given his past, nothing would surprise me. Also, we don't know who gave the funeral home this information either. For example, when my Dad died, the funeral home director asked for parents' names, etc. My stepmother had no idea. Luckily, I was there with the correct info. This is why you see death certs with "don't know" as the parent's names, etc. All you can do is hope that people are giving the correct information.
Btw - I noticed that Carol Ann Burgess (b. 1942) isn't listed in the funeral book. Maybe they just didn't bring her?