No, definitely not, although I do think I've seen a few people on here say they prefer to just use the regular paper. I've seen quite a few pictures on this site with the Universal Game Cases opened up flat with custom art inserted, and they all have no bleeding. So either the majority is using the heavy matte paper, or there's just a site I'm overlooking to order the glossy paper from.
Haha, either way, I'm sure somebody will come along sooner or later with a link.