In Methods of Homological Algebra before Proposition III.3.5 there is a short comment: "The next proposition shows that any exact triple [of complexes] can be competed to a distinguished triangle".

How should one understand this comment?

In other words, given exact sequence of complexes in abelian category $\mathcal A$:

$$0\rightarrow K\stackrel{f}\rightarrow L\rightarrow M\rightarrow 0$$

with no conditions on maps and complexes, is there always a way to construct a map $M\rightarrow K[1]$ and isomorphism (in the category $\operatorname {Com}(\mathcal A)$) of the obtained triangle with the distinguished triangle

$$\rightarrow K\rightarrow \operatorname{Cyl} (f)\rightarrow \operatorname{Cone}(f)\rightarrow K[1]\rightarrow$$

Proposition III.3.5 is a construction of quasi-isomorphism between the exact triple and $0\rightarrow K\rightarrow \operatorname{Cyl} (f)\rightarrow \operatorname{Cone}(f)\rightarrow 0$, but how is that related to the comment?