I've heard that one before, but I'm fairly sure it's not actually true. "arigato" is usually written in hiragana (there's also Kanji for it, but I don't know them), and the usage predates the Portuguese -- apparently an early form of the word appears in the Tale of Genji. And if you think about it, it only sounds similar to someone who speaks English; the Japanese would have emphasized the "b" sound much more where we just sort of skip over it.

It's such a bizarre coincidence, though, that it feels like it should be true!