I've heard of this example before, and this is speculative but I wonder if it's because the speaker is counter-intuitively also the object of the phrase.
The root "obrigad" sounds a lot like the English word "obligate". If this is more than just a coincidence, then a more direct translation is "I am obliged" rather than "thank you". Said this way it makes a lot of sense why the verb is determined by the speaker.