No, it's documented, as is tempura. It's like pancakes: you make them before the time of fasting. "The Time of X" in Spanish is "tempora X" and I would bet Portuguese is similar.
> evidence indicates arigatō has a purely Japanese origin
I remain suspicious, though. Maybe what happened was the popularization of an existing Japanese term under the influence of Portuguese Jesuits, since it sounded similar to obrigado?
Perfectly possible. I think I've seen evidence elsewhere of similar but unrelated words influencing each other. For example, round about where I live the Romany word "shan" is used meaning "mean" or "worthless", but it seems to have been influenced by the unrelated "sean" in Gaelic (also pronounced "shan") which means "old". So it's come to mean something worn out as well.
There are loads.
https://en.wikipedia.org/wiki/List_of_Japanese_words_of_Port...