Even so, I think nearly all of the people saying they’ve done it are probably just saying they’ve used saliva to remove blood and it seems to work.
I think what’s happened here is probably that “If you get blood on something, you can use saliva to remove it” got modified to “If you get blood on something, you can use your own saliva to remove it” pretty much superfluously, then with a couple of accounts like yours (where we still haven’t eliminated other factors) reinforced the term ‘your own’ as being a crucial criterion.