By that definition then the Premier League is also still a cup competition.
UEFA also disagree with you as they define the Champions League thus:
http://www.uefa.com/MultimediaFiles.../Regulations/01/63/02/44/1630244_DOWNLOAD.pdf
This confirms that the Champions league is preceded by the Qualifiers and that they are not the League Proper.
1.01 The present regulations govern the rights, duties and responsibilities of all
parties participating and involved in the preparation and organisation of the
2011/12
UEFA Champions League including its qualifying phase and the
play-offs (hereinafter the competition).
II Entries – Admission – Integrity of the Competition – Duties
Article 2
Number of clubs per UEFA member association
2.01 UEFA member associations (hereinafter associations) may enter a certain
number of clubs for the competition, in accordance with their position in the
coefficient rankings in Annex Ia, drawn up in accordance with Annex II of
these regulations. However, no association may enter more than four clubs
for the competition. These rankings also determine the stage at which clubs
join the competition.
2.02 Associations are represented on the following basis:
a) One representative: winner of the top domestic league championship.
b) Two representatives: winner and runner-up of the top domestic league
championship.
c) Three representatives: winner, runner-up and third-placed club in the top
domestic league championship.
d)
Four representatives: winner, runner-up, third- and fourth-placed clubs in
the top domestic league championship