I don't see the relevance of the question?
It's obviously a much greater achievement to win the Premier League and Champions League than the former and the FA Cup. In this case the term "the double" does not carry the same weight as the term "the treble" because the FA Cup is by some distance the least important of the three trophies.
"The double," however, does refer to something specific, even if it's not exactly an uncommon achievement in England (unlike "the treble"). So it should be reserved for a team winning the League and FA Cup only.
Winning "the treble" is, and has always been, a case where a team wins the League, the Champions League and the FA Cup. That is what it means. It is so prestigious because it has only happened once in England (to the best of my knowledge) and is rare even across the whole of Europe, and because it includes winning the only two trophies that matter to the clubs at the top end of football.