A false bottom with a layer of whole hops might also be filtering out break material.
When I had a hop stopper and plate chiller, the hot break and pellet mush would stay in the kettle but the cold break ended up in the fermenter. Now that I've scaled down, I chill everything in the kettle and don't bother with a screen, but I rarely wait long enough for all the break to settle. End result is about the same in terms of wort clarity. There's break (white, not green) in suspension in the hydrometer sample that I take at the start of transfer, which settles down to about an inch or less within 10 minutes, revealing clear wort. It never makes a difference.