Just to clarify, prior to Liverpool in 2005, a precedent had already been set when Real Madrid finished 5th but won the CL in 1999-2000 - their association put 4th placed Zaragoza in the UEFA Cup and 5th placed Real Madrid into the Champions League. Real Madrid had a good UEFA rating/coeficient so went straight into the group stages.
AFAIK UEFA had assumed that the English FA would follow this model in 2005, but instead the FA decided to play silly buggers and put Everton through, and then lobby on Liverpool's behalf. Everton's coefficient wasn't enough to put them straight into the group stages, so they had to play a qualifier against Villareal, which they lost. Liverpool were let in as defending Champions, but had to play every qualifying match from round one. However, as Liverpool had a good coefficient, having won the UEFA Cup in 2001, they got a relatively easy route, although they weren't afforded country protection for the group stages, and ended up in a group with Chelsea. For some reason, a lot of people assumed that Liverpool's involvement meant that Everton got a harsh draw, but that was never the case.
UEFA changed the rules to prevent an association from playing silly buggers again.