That's not even close to the logical conclusion: the statement was "Enforce minimum wages that people can actually live on", not "Higher minimum wage is always better."

Contrast that with many right wing arguments about taxation, which usually take the form "Lower/more regressive taxes are always better, and here's why" - disturbingly many of those arguments are "valid" (i.e. if you accept the arguer's claims, the conclusion follows) no matter what the starting point is, and the end result would either be zero taxes for everyone or (surprisingly common) almost 100% taxation of the lower classes and no tax on the upper; hell, if we allow for redistribution, many of the conservative arguments actually imply that the upper class should be given money by the lower class, for the good of the economy.

If your argument pushes some number in one direction but doesn't turn around for some value of that number, then there's typically a problem with the argument; here, that's not the case, the poster explicitly provided that stopping point.