My bimac Davy Jones was VERY strong for his size. from my experience, just about all octos seem to investigate around the surface at least once in a while. you might want to put heavy objects on top of the lid, but then it may look "unkempt."
i once saw a documentary (Ultimate Guide: Octopus) a couple years ago that said an octopus can lift up to 40 times its weight. it's probably a bit of an exaggeration, but it's something to keep in mind when trying to keep the little suckers in (pun intended).
There's a picture I've seen (in Wells, maybe) of a vulgaris who died because it pushed its tank lid up enough to make a crack it almost fit through, but it got stuck at the beak. I don't think this is common (I've never heard of it here) but it does suggest that schemes that only allow a little crack to open can still be a problem.