Does a stunned creature roll Initiative with disadvantage?

Question

Part of our group got stunned before Initiative was rolled:

Stunned

• A stunned creature is incapacitated (see the condition), can’t move, and can speak only falteringly.
• The creature automatically fails Strength and Dexterity saving throws.
• Attack rolls against the creature have advantage.

Incapacitated

• An incapacitated creature can’t take actions or reactions.

Even though neither condition states that checks are made with disadvantage, our DM ruled to roll Initiative with a disadvantage since they can't move or take actions. This made sense to all of us, but we are wondering what the ruling by RAW is.

Answer 1

You pretty much answered your question yourself...

It's not part of the stunned and incapacitated conditions.

...BUT...

There's this sentence you can find in the Player's Handbook p.173:

The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.

So...

...your DM did it right.

Answer 2

Initiative is a matter of timing, and does not depend on your condition.

Unconscious creatures have their initiative positions, if only to determine when they roll a death save. Even if a creature is unconscious (whether asleep, or from some other cause) they would roll initiative as normal, for figuring out when they wake up, when they stop being surprised and regain their reactions, etc.

Neither stunned nor incapacitated has any effect on initiative. A creature with those conditions may not be able to do very much when his turn comes, but still has a timing slot, even if it is only to determine when they get to make a saving throw to end the condition, or to define when the condition ends.