Should octopus be cooked twice? When I see any recipe for octopus, it's almost always boiled first. Harold McGee says to chuck it in the oven (dry)

The point is, when ever any one fries/BBQ's octopus, they always fry/BBQ cooked octopus. 

My question is about why does it have to be this way? My research potentially suggests one of 2 things, but I'm unsure.


By boiling/oven first, you get a more even cook
Frying only would make it chewy


In my case, I don't (think) I want to cook the entire octopus, but instead, semi defrost it (until I can chop the arms off (so it would remain mostly frozen)), remove the arms, refreeze and cook the arms as and when needed

If I were to cook an arm only by frying, is there any danger here or do people cook it twice (when frying) for taste/texture?
Actually, Harold McGee supports brine-and-simmer as an alternative to baking, and explains the texture-related goal behind both: octopus contains a lot of connective tissue, and both that and the muscle need to be softened.

I've read elsewhere (can't remember the source right now) that octopus muscle fibres contract and drive out their water at unusually low temperatures, such that the ideal cooking temperature is 55C. You're going to want long cooking times at those temperatures, so we're talking either sous vide or deep-fat frying in a temperature-regulated fryer.