equal = being better?

Scalar comparison of equality indicates “at least equal”
In the absence of indications to the contrary, a scalar [= ‘clever’ in [i] below] comparison of equality is interpreted as “at least equal”, not “exactly equal”:

i) Jill is as clever as Liz. [Jill may be cleverer]
ii) Jill isn’t as clever as Liz [Jill must be less clever]

Example [i] is consistent with Jill being cleverer than Liz: we can say Jill’s as clever as Liz, somewhat more so in fact. [n] Scalar equality therefore normally exclude only the relation of inferiority: it gives a lower bound. . . . . .

[n] This can indeed apply also to equal itself, as in Kim is the equal of Pat when it comes to solving crossword puzzles (which is consistent with Kim being better) or We hope to equal last year’s profit (consistent with bettering it). (CGEL, p.1100~1101)

1. as ~ as:
Does the phrase “at least equal” refer to as ~ as construction or one of *as*s?
(I want to know whether the meaning comes from the structure or the lexical meaning.)

2. equal:
I don’t find any lexical source that equal implies being better. Is there any dictionary saying the meaning?

• You're mistakenly assuming "Jill is as clever as Liz" means the same as "Jill is at least as clever as Liz". In actual fact, if people really have that second meaning in mind, they'll normally either include at least, or they'll say something like "Jill is as clever as Liz - if not cleverer" (or maybe more clever, since that particular adjective doesn't sit well with the -er suffix). Sep 1, 2013 at 14:55
• Yes, I'm with FumbleFingers on this one. Despite the text you've quoted, I would naturally assume that "Jill is as clever as Liz" means that the two are equally clever, or quite nearly so. If I meant something different, I'd add qualifiers. Sep 1, 2013 at 15:55