I'm confused. There seems to be two different conversations going here. One is talking about the seam that is created when you sew a border to the quilt top. The other conversation is about the seam that is created when you don't have enough length of fabric for your border and need to sew two pieces together.
When I'm sewing my border on the quilt top I press to the border side because there is usually less bulk that way.
When I'm joining two pieces of fabric to get the length of fabric I need for the border I sew on the bias (45 degree), trim my seam and press open. The seam becomes nearly invisible that way. I do the same when joining for binding.