Could I cast Summon Monster to appear just on the other side of a door for instance, or while beneath the ground via a burrow?
Line of Effect: A line of effect is a straight, unblocked path that indicates what a spell can affect. A line of effect is canceled by a solid barrier. It's like line of sight for ranged weapons, except that it's not blocked by fog, darkness, and other factors that limit normal sight.
You must have a clear line of effect to any target that you cast a spell on or to any space in which you wish to create an effect. You must have a clear line of effect to the point of origin of any spell you cast.
Summoned creature is an effect produced by a spell - an unbroken line of effect between the caster and point where the creature will appear is needed. Solid barrier (like doors) blocks line of effect so the answer to your question is "no" but for slightly different reason than the thread title implied.
I certainly thought this was Loss of Sanity to Summon. Apparently I've been playing too much Eternal Darkness...
Not that this helps with answering your rules question, mind you.