You are both slightly right and wrong.

It's not the fact that the monitor has an HDMI 2.0 port that makes the difference, not entirely. It's that some 1440p displays support downscaling from 2160p (e.g. Dell U2518D and Samsung CHG70).

Let's say a game always renders in 1440p.

If you have a 1440p monitor that doesn't support downscaling:

PS4 set to 1080p with SS

• PS4 renders 1440p
• upscales to 2160p
• renders HUD in 2160p
• downscales everything to 1080p -> 1080p via HDMI to display
• Display upscales to 1440p

If you have a 1440p monitor that does support downscaling:

PS4 set to 2160p:

• PS4 renders 1440p
• upscales to 2160p
• renders HUD in 2160p -> 2160p via HDMI to display
• Display downscales to 1440p

So in short: If your display supports downscaling from 2160p scaling is

• 1440p ->2160p -> 1440p

if it doesn't support downscaling it's

• 1440p -> 2160p -> 1080p -> 1440p.