I'm seeing a disconnect you could drive a truck through, here. Silliness = lighthearted, no? When you are being silly, you are generally smiling and/or having fun, therefore depression is a bit mutually exclusive.
The depressing world without relief is the grimdark without the silliness, not the grimdark that doesn't take itself too seriously and is packed with whimsy.
Perhaps I misunderstood, from my reading of the original post, the statement seemed to be something along the lines of:
"Any form of unrealism is silly and not suitable for a D&D world, and every world should take every aspect of itsself with true realism total seriousness."
Silliness is, generally, lighthearted good fun, though as I said, it can go to far, though even when it does, taking sillyness too far can be more enjoyable than taking seriousness too far.
But, as I said, it's not just sillyness that keeps a game lighthearted.
Take for example the portrayal(and physical appearance) of Tieflings. In most medieval settings, these people would be murdered on sight and hunted to extinction as fast as possible. Only the greatest sums of money or political leverage could prevent this and even then, it would probably be short lived and the people immune to those things would likely be waiting for a chance to stab you in the back.
This can be applied to almost any non-human race, and even to the varous ethnicities of humans. Avoiding this generally involved glossing over humanity's "scared and fearful" nature. Which entails avoiding a lot of political, military, and social issues as well. Avoiding these things helps keep the game lighthearted, even if delving into them is interesting.
Perhaps this is all misunderstanding the OP, but it seemed to imply "true", that is, AD&D, it was more important to establish a "serious" world, than to have a fun game, which is the goal of BD&D.