How did 'cigarette paper' shift to signify strife?

Source: Rebecca Gowers. Plain Words (2014 ed). p. 208 Middle.

  Note. Gowers also wrote under this heading: ‘About the age-
long conflict between it is I and it is me, no more need be said
than that, in the present stage of the battle, most people
would think “it is I” pedantic in talk and “it is me” improper
in writing’. Now, however, most people would find ‘it is I’
disquietingly fey in any modern context, written or not. By
contrast, the grammatically needless use of myself is
flourishing. The Deputy Prime Minister, for one, clearly
believes that myself confers a certain something that I and me
both lack: ‘Myself and the Prime Minister are saying exactly
the same thing’; ‘There is not a cigarette paper between
myself and the Prime Minister on this issue’, ‘But all of us in
this government, including the Prime Minister and myself,
are not willing to compromise …’ etc. ~