Correct usage of "than" or "as" when comparing two things

I've found a cited example of incorrect usage in Bill Bryson's "Troublesome Words" which I don't understand because he doesn't explain it, and even going back to the source (Ernest Gowers' "Plain Words") doesn't help.

Apparently, the sentence "nearly twice as many people die under 20 in France THAN in Great Britain" is wrong because it should read "AS in Great Britain".

Could someone please tell me why this is wrong and, if so, explain how you know when to use "than" and when to use "as"? I'm driving myself mad second-guessing myself every time I use "than" in case I should be saying "as"! Thank you.

Comparisons of equality or similarity use as to introduce the entity you're comparing your topic to:

X is just as big as Y.
This answer is the same as Joe's ...

This is true even if the equality or similarity is denied; not takes the whole comparison into its scope:

... but it is not the same as Anne's.

Comparisons of inequality or difference use than:

X is bigger than Y.
This answer is less complete than Joe's ... but it is not less complete than Ann's.

Some comparisons use different prepositions: different itself uses to and from as well as than. But than and as don't flip.

The sentence you quote looks like a comparison of inequality; but the twice is a quantifier just like the negators (not) in my "answer" examples, and like those negators it takes the entire construction in its scope:

How many people die under 20 in Great Britain?
2x, where X equals the number of people who die under 20 in France.

It is thus a comparison of equality, and uses as ... as.