Being on the rim never lets you ignore other squares of elevated terrain.

A . . . . B . . . C
. . . . . . . . . .
E E E E X E E E E E

Characters A, B, and C are all on level 1. Character X is on level 2.

Character X can only draw LOF to B (and vice versa). This is because the elevated terrain on either side of X will block LOF to A and C.

The situation with the corner above is no different. Other squares of elevated terrain can and do block LOF and, in the case of the original question, those squares just happen to be right across the diagonal of where you want to draw LOF.

Here is the easiest method to use to determine whether any line of fire across any intersection point is clear, hindered, or blocked.

Imagine that there is a string connecting the two squares at the endpoints of the LoF.
Pretend that you put your finger on the string at that intersection and bend the string a bit so that it crosses one of the two squares of the intersection. Make note of what that LoF would be.
Do it again to the other side.
The LoF is the lest restrictive of the two results.

I think more like, "rules trumps video game thinking".

You draw lines of fire from the centers of each square. I think too many people assume that you can tuck yourself into the little corner of your square and shoot from there. That's what I do when I play CoD!

Unfortunately, you have to assume the character is actually standing a bit away from the corner, and while in real life they may have some line of fire on that diagonal from a distance, they would not be able to see someone down on the lower level opposite them in that corner.

Clix also does not have a way to give you LoF at longer distances, so it has to just be blocked. (Because who wants to deal with the formulas involved with what that would have to be!)

Ah, okay. I thought that Doop was on the lower elevation.