Mistake in Wikipedia CSG example? I'm confused about the example given in Wikipedia article about Context-sensitive grammar:

https://en.wikipedia.org/wiki/Context-sensitive_grammar

Disclamer: I've already changed discussed section in wikipedia article, so current state of article will differ from what I'm discussing in this question. Original version is here: https://en.wikipedia.org/w/index.php?title=Context-sensitive_grammar&amp;oldid=747616366


  The following grammar, with start symbol S, generates the canonical
  non-context-free language { anbncn : n ≥ 1 } :
  
  
  S       →       a   b   c
  S   →   a   S   B   c
  c   B   →   W   B
  W   B   →   W   X
  W   X   →   B   X
  B   X   →   B   c
  b   B   →   b   b
  


They do not claim directly that this grammar is context-sensitive, but next sentence implies that that they consider it as context-sensitive:


  rules 3 to 6 allow for successively exchanging each cB to Bc (four
  rules are needed for that since a rule cB → Bc wouldn't fit into the
  scheme αAβ → αγβ)


So they appeal to the canonical form of context-sensitive grammar rules: αAβ → αγβ, implying that whole grammar is context-sensitive. 

What I'm confused about is rule #3, which seems to be not fitting scheme αAβ → αγβ. I consider terminal $c$ here as part of $\alpha$, variable $B$ as $A$ in scheme, $\beta$ is empty. This implies that $cB$ can not produce $WB$, as $c$ should be saved on same place ($cB\rightarrow c\dots$).

Did I missed something or this grammar was really placed here mistakenly (as it is not real context-sensitive)?
If I am not mistaken, a simpler CS grammar is possible.  Here it is:


$S \rightarrow ABSc$
$S \rightarrow Abc$
$BA \rightarrow XA$
$XA \rightarrow XY$
$XY \rightarrow AY$
$AY \rightarrow AB$
$A \rightarrow a$
$Bb \rightarrow bb$.


A derivation for the string $aaabbbccc$ is

$\Rightarrow_1 ABSc\\\Rightarrow_1 AB\textbf{ABSc}c\\\Rightarrow_2 ABAB\textbf{Abc}cc\\\Rightarrow_3 A\textbf{XA}BAbccc\\\Rightarrow_4 A\textbf{XY}BAbccc\\\Rightarrow_5 A\textbf{AY}BAbccc\\\Rightarrow_6 A\textbf{AB}BAbccc\\\dots\\\Rightarrow_{3-6}AAB\textbf{AB}bccc\\\Rightarrow_{3-6}AA\textbf{AB}Bbccc\\\Rightarrow_{7...}\textbf{aaa}BBbccc\\\Rightarrow_8 aaaB\textbf{bb}ccc\\\Rightarrow_8 aaa\textbf{bb}bccc$