"strongly relational m-consistency when the domains contain at most m elements implies satisfiability" plain wrong?
Yes, the quoted statement is correct.  Wikipedia gives a proof in the next four sentences that immediately follow the quote you gave.

The constraints that arise from 3-colorability are not strongly relational 3-consistent, so the quoted statement implies nothing about 3-colorability.  Consequently, there is no contradiction.

(Why aren't the constraints from 3-colorability strongly relational 3-consistent?  Consider a star graph, with a vertex $v$ that is connected to three other vertices $w,x,y$.  There is one constraint per edge in the graph: e.g., one constraint that constrains the colors assigned to vertices $v,w$; one for $v,x$; and one for $v,y$.  Suppose we have a partial assignment that assigns $w$ the color red, $x$ blue, and $y$ green.  Then there is no way to assign a color to $v$ that makes the three constraints for $vw$, $vx$, and $vy$ all valid.  Thus, the constraints do not satisfy the definition of strongly relational 3-consistency.)