Pinnacle is the brand name put on Woodcraft's arkies, but the box and instructions inside are identical to Dan's.
I assume that this refers to the current production. If so, then we know what that means. As I recall, Natural Whetstones pamphlets are similar as well.
It certainly won't hurt your blades. I'd worry about it possibly allowing bacterial growth, but I could be wrong there. I just assume rancid fats have that risk. Anyway on the stones, yeah it doesn't matter as long as you clean it off. Olive oil does go rancid far, far, far, far, faster than sperm oil. In fact I think sperm oils stability after boiling was one reason why it was so popular. It's not that olive oil is so bad you can't use it. Just that mineral oil seems better and isn't any more expensive, so I'd go with it.
Fair enough, but who knows what kind of bacteria I'm transferring to a strop when I rub it with my palm prior to stropping. After shaving, I dip the blade in a solution of 1 pt. mineral oil to 4 pts. denatured alcohol. Prior to stropping, I wipe the blade off with a bar towel then spritz it off with isopropyl alcohol. My guess is that the bacteria is coming from my hand.