Those are not counter examples. Tribal affiliation is determined along one gender line - when of course any given person has many ancestors among mixed gendered lines. For instance, Take one's great grandparents. There are 8 of them. One is one's father's father's father. The others are:
father's father's mother, F M F, F MM, M F F, M F M, F M F, and Mother's mother's mother.
Only one of them will determine one's tribal affiliation - the other 7 can be from any tribe. Next level up and you have 16 great great grandparents - again only one determines tribal affiliation, and the other 15 might be from any tribe - and could thus be descendants of David, and if so, then of course the people in question are descendants of Kind David.
Going back shows how quickly these numbers go up - 16, 32, 64, 128, 256, 512, over 1000, 2000, 4000, 8000, over 1 million, etc.
This is why those people you mentioned are certainly descended from King David, who lived 1,000 years before hand, had hundreds of children, & thousands of grandkids, with another 40 generations of exponential growth before Jesus' day. This can be a tricky idea for many people today to realize, so let me explain further.
For instance, Thomas Jefferson has literally thousands of descendants alive today, even though he only had a few kids (many less than King David!). Ever year, some of those descendants marry, and all their kids are Thomas Jefferson descendants. So in a few centuries, nearly everyone in the US will be a descendant of Thomas Jefferson, and a few centuries after that, nearly everyone in the world will be, and shortly after that, every single living human on earth will be a descendant of Thomas Jefferson. The same goes for anyone who has a few kids, unless all of the descendants die childless soon (after a few generations, that's increasingly unlikely). Think about it. It's pretty cool! That means that you and I are both descendants of King David, as is nearly everyone today (except, perhaps, some Australian Natives, and maybe some people in Asia & Africa, some isolated Amazonian tribes, etc.
The same math applies to people like Genghis Khan, pharaoh Ramses II, etc. It's also explained the scientific paper
http://www.nature.com/nature/journal/v431/n7008/full/nature02842.html .
In Christ-
Papias