Interesting. Money in the US has "In God We Trust," and it's not inherently religious. So I'm not sure the proclamation makes Thanksgiving religious. The origins might, though. I don't know enough about it to tell, and I'm not sure I care enough to research it. I don't really celebrate it as other than a day off from work though. Travel is a nightmare at that time, and, although this may sound like humblebragging, I try to be grateful at all times anyway.
Could be going down the rabbit hole with this comment, but cancer is an extremely generic term - lots of different organ and cell types. And smoking is also less well defined than one might think - additives to cigarettes and paper are not, I believe, considered in most studies. And not all smokers develop cancer. I had two relatives who were heavy smokers and lived until their late 80s and didn't die from cancer. To summarize, there is lots that we don't know about cancer.
So I would agree that this could be out of the box thinking that could have some truth to it. But I also doubt that research will be done in that direction unless there is some proof that justifies the expenditure. So we're likely to not know for sure, and most will assume it's not true.
Many of the people who participated in these events are realizing the consequences, and trying to hide their actions. Good for these groups for preserving the records.