Yep, that cambium will break under tension pretty easily and it might take some of your wood with it so its a good Idea to remove it.
I like to take the thick outerbark off first with my hatchet, then when its just the cambium like that I'll take my mora, start in the middle and get a good bite
just above the wood then push down with the knife and work it back and forth using the stave as a fulcrum if the cambium is fighting back. Then finish with a little scraping and you're done.
I've tried the peeling thing but it doesn't work on every stave for me so I stick to the above method and it usually works out allright.