In A Song of Ice and Fire and Game of Thrones, children born to a noble parent, but out of wedlock, are given special "bastard" surnames. They are openly acknowledged as the children of a noble, and it's generally expected for their noble parent to take care of them in some way, but they have none of the inherent legal rights of trueborn children.
In the novels, any child born to a lord or lady, who's other parent is not that lord or lady's spouse, is acknowledges as a "bastard-born". Most of them involve Lords having affairs with commoners, but not all. For example, Aegon IV had tons of bastards, with both common and highborn mothers (all of which he legitimized on his death.) This lines up with the "normal English" definition of the term bastard as well.
However, in the show, as far as I know, all of the acknowledged bastards we have seen have highborn fathers and lowborn mothers:
- Jon Snow -- everyone thinks he's Ned's son by a barmaid.
- Ramsay Snow -- Roose Bolton's son by a miller's wife.
- Obara Sand -- Oberyn Martell's daughter by a peasant
- Nymeria Sand -- Oberyn Martell's daughter by a foreign woman
- The other Sand Snakes -- Oberyn Martell by Ellia Sand
Other characters with bastard surnames are mentioned but, as far as I know, we don't learn enough about them to know if their parents were both highborn or not.
So, my question is, is the child of two unmarried, but highborn, parents still considered a "legal bastard" in the TV universe? Have we seen a single acknowledged example of this on-screen?
The reason I'm asking is because:
someone contended that Jon Snow isn't really a bastard, since both his parents were nobles, and I contend they are wrong, he is really Jon Waters.
Thus, a claim has been made that a child of two noble unwed parents would not get the usual "bastard" surname because both their parents were nobles. I am looking for proof that this isn't true in the show.
UPDATE:
To address the current comments and answers:
I know what the English word "bastard" means. In the Game of Thrones universe, though, there is a special class of "bastard" that has noble parents -- they get a last name, for starters. My question is about those children of two unwed noble parents.
I also what the novels have to say, (which I called out in my question), and there the answer is trivial because we see plenty of bastard-born children with two noble parents. But for this purpose, the novels are irrelevant -- I'm looking for evidence specifically from the TV show, and so far, every instance I have come up with was cut from the show.
(For the record, I'm 100% positive that it doesn't matter but that isn't proof.)