It's just my opinion, but based on experience, I'm with Richard, but with a qualification. I think that the bowl picture is spalting, but notice that it is only in the sapwood. I've never seen spalting of the heartwood in Osage....that's not to say it doesn't happen, but I've never seen it, nor have I seen it in photos of finished turned products.
Spalting is the beginning stages of decay, and what I understand is that the black lines are the boundary lines between colonies of fungi. Since Osage heartwood is tremendously resistant to decay, it would be extremely rare to find spalted heartwood. I don't think that what is being called spalting in the photos of the heartwood turning blanks is truly spalting.
Just my two cents worth.
Danny