Hmmm... I wonder if it's just a matter of a faulty description of "Captains of the Black Flag". For challenges ("The Tenth Wave"), only some of the tasks count.

I'll have to ask about it. Probably won't get an answer before Monday.

Yup, I was right: the same stuff that counts for Challenges also counts for War. The key here is that it says "points", which the last 4 items in the War/Challenge report are not (they are... "counts", I guess?).

"The Tenth Wave" explains it better, but that's all that it is: an extra explanation (hence the parentheses). "Captains of the Black Flag" simply lacks the extra details, but it counts in exactly the same manner.

Before you say that it's inconsistent and/or confusing, I agree, but that's how it is and there isn't much that we can do about it.