Does mounted combat require a willing rider as well as mount?

A party is traveling on a path through a woods when they are simultaneously attacked by a group of orcs and a single, overly-clever ogre. The ogre grabs the party’s fighter (successful grapple attack) and announces his intention to move 20 feet (speed halved) among the orcs, subjecting the fighter to multiple opportunity attacks as she leaves their reaches.

"Wait!" protests the fighter. "The opportunity attacks rule says…

You can make an opportunity Attack when a Hostile creature that you can see moves out of your reach…[but you] don’t provoke an opportunity Attack when you Teleport or when someone or something moves you without using your Movement, action, or Reaction.

"Since you are moving me, the orcs cannot attack me as you drag me past them."

"Hmmm…" considers the ogre. Knowing full well that specific beats general, he tries to think of a case in which something can explicitly provoke opportunity attacks even if it is being moved. "Aha!" he says brightly. "The grapple rules say…

When you move, you can drag or carry the Grappled creature with you

The ogre easily flips the fighter across his shoulders. "Now I am carrying you."

"That doesn’t matter."

"If I am carrying you, I can be your mount. And the mounted combat rules say…"

if the mount provokes an opportunity attack while you’re on it, the attacker can target you or the mount.

"That’s ridiculous," says the fighter indignantly. "First of all, you can’t provoke an attack of opportunity from the orcs unless you and they are Hostile, and clearly you are allies."

"You don’t know that," says the ogre. "We are actually from different tribes, and it was a coincidence that we both ambushed your party at the same time. If we win, I expect we will fall to fighting one another over your loot." The orcs nod in agreement. "Besides, the DMG definition of Hostile is…

A hostile creature opposes the adventurers and their goals but doesn’t necessarily attack them on sight.

"Setting aside the adventurer-centric language, as NPC’s these orcs and I oppose one another’s goals. As I move around, they could certainly choose to attack me rather than you."

"Point taken – but you still can’t be my mount."

"Why not? The Mounted Combat rules say…

A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount, using the following rules…"

"I am a willing creature," says the ogre, "I am at least one size larger than you, and, as you will note from your position atop my shoulders, I have appropriate anatomy. It is still my combat turn, and I say that I am your mount."

"That’s not for you to decide! I mean, you can’t be my mount against my will! It says a creature can serve as a mount, and you are most definitely not serving me."

"There’s no game definition of serve."

"Right, so we go with the common English meaning of ‘being in service to’, ‘following commands’."

"I rather prefer the English meaning of ‘able to be used as’; like after the orcs kill you, your helmet will serve as my chamber pot."

The rules make it clear that to be a mount, the creature has to be willing. But does the rider have to be willing as well?

And if the rider does have to be willing, does that mean a rider that has been rendered unconscious no longer counts as a rider for the purposes of mounted combat? (an unconscious person on a moving horse could not receive opportunity attacks because they could no longer consent to be a rider?)