I think the thinking is that the thermal path has the smallest cross-section at this point in the train.
I don't do any high performance modding or anything, but I just tin the pads with regular solder. When I solder it, I let it flow/self-center, and then push it straight down with an appropriate tool to squeeze out as much solder as I can from between LED and solder pads. This is probably along the same lines of "does it really matter?", but it makes me feel better about it, and it's MY light, so I do what I feel seems best to my ability.
With regards to the refrigeration of solder paste, I imagine it is to keep it from separating out, since you can't very well stir the contents of a syringe if it separates. BUT that is just a guess on my part.