Although Japanese took several words from Portuguese, arigatō does not come from Portuguese obrigado. The word arigatai existed in Japanese long before the Japanese ever encountered Portuguese. The sentential form of arigatō, namely arigatashi "unlikely to be; rare; welcome" shows up written in kana in the Man'yōshū, an 8th century poetry collection. It shows up, for example, in the form arigataku in Genji monogatari, an early 11th century novel. It shows up already as arigatau in Heike monogatari, a 13th (? 14th?) century epic. There is no question of the pure Japanese pedigree of the word. Similarly, "obrigado" in Portuguese comes from Latin "obligare". The change from l to r is typical of Latin-derived Portuguese words.
But one shouldn't need to know that! The hypothesis is absurd on purely phonological grounds. Why on earth would Japanese hear "obrigado" and say arigatō instead of oburigado?