The argument will fail
under Section 1 of the Charter. The Charter allows restriction of certain rights, when the objective is reasonable (R. v Oakes). The Charter is very different from the US constitution in that respect.
The real argument that Rogers makes, buried beneath the click-generating headline (at the source), is that their testing showed their claims to be true, and therefore said claims did not violate the Competition Act. This is the argument on which I think they have a chance of success (reality notwithstanding).