Again, that's a question of legality.There seems to be a regional acceptance for handling different creatures. We are relative newbie divers, but I've seen divemasters grab octopi and pull them out of their holes, yet scold people who try to touch turtles.
In my example, I have heard that turtles can contract diseases from contact, so maybe that's the reason we shouldn't touch them.
For me, I'd rather leave everything alone since I'm in their house. I'd hate for an octopus to come into my house and twirl me above his head and bounce pass me to his buddy.
Touching turtles (at least the Hawaiian Green Sea Turtle and the Hawskbill Turtle) is illegal, mostly due to their endangered status.
And that brings us to the next point: octopi aren't endangered. At least not the ones around Hawaii.
While I do tend to be respectful of the underwater life, there are occasions whereby it is acceptable to interact. I don't agree with "digging octopi out of their holes" but it has been pointed out that these animals are capable of great things. If they don't want to be played with, they won't be.
I've heard stories where an octopus has been captured alive and placed in a bag. A few minutes later, two other octopi have caught up to the diver... one has begun harassing the diver around the mask / reg area, another is quietly and cautiously opening up the catch bag and letting out the captured octopus.
Bottom line: if they don't want to be played with, they won't be.