Rules Check: Small PC Riding a Flyer Battle Familiar — Does Flyby Protect the Rider Too?

I've been working through a rules interaction and want a sanity check before I bring it to my table. Here's my reasoning — please poke holes in it if I'm missing something.

The Setup

Battle Familiar (spell) lets you pick a form for your familiar: Brute, Flyer, or Stalker. I'm looking at the Flyer form specifically.

Flyer Battle Familiar Stat Block:

• Size: Medium
• Flyby: The familiar doesn't provoke an Opportunity Attack when it flies out of an enemy's reach.

My Reasoning Chain

1. The Flyer form of the Battle Familiar is a Medium creature.
2. A Small character can ride a Medium creature (mount size rules).
3. So a Small PC could mount the Flyer battle familiar.
4. When the familiar uses Flyby to fly out of an enemy's reach without provoking an Opportunity Attack, the rider is being carried along — and since the rider isn't choosing to move under their own power, I'm treating this as the rider undergoing forced movement.
5. Therefore, I'm concluding the rider also avoids provoking an Opportunity Attack in that moment, because they're not the one taking the "leaves reach" action — the mount is.

So: does Flyby on the mount effectively shield the rider from opportunity attacks too, on the theory that the rider's movement is "forced" by the mount?

Forced Movement isn't an official term in 5e. The rule is that you avoid an opportunity attack "when you are moved without using your movement, action, Bonus Action, or Reaction."

This appears to apply to mounted movement, at least normally (it's an open question what happens if you have a steed that you need to spend actions to command).

Also, the riding rules aren't actually that well put together. (Fun fact: they don't actually say the rider moves with the mount at all.)

@Allinar There's also this conversation from the Dev (5e era):

@ChewBobcca if a mount takes the Disengage action does the rider provoke opportunity attacks?
@JeremyECrawford No, since the mount isn't provoking them and the rider is being moved by someone else's movement (PH, 195)

A subtle change between editions is that the text "In either case, if the mount provokes an opportunity attack while you're on it, the attacker can target you or the mount" is not present in the 5e Mounted Combat rules, so IMO, with the new rules, if a mount provokes an OA, the potential target is always the mount.