Great read.
Just to try and clarify the 'giants' part a bit: this comment I first saw in the media by the owner of the club. He said that they were either hoping for a 'weaker' group if that's possible at all to try and get some points from the home games, or at least two 'giants' with a lot of supporters in Hungary who would no doubt help to fill the entire stadium for all matches.
While Liverpool is one of those giants in Europe, and every true football fan remembers at least the comeback in Istanbul, a team like Barca or Milan could attract even more neutrals and more easily to go and watch them play. It's mainly about financial reasons, no disrespect here. I expect a sellout anyways for Debrecen - Liverpool, but not so sure about the other two games.