I think this discussion is on track vis-a-vis concentration and temperature. Concentration affects reaction rate but not the rate constant while temperature does change rate constant.
The rate constant reflects the fraction of reagent, if you picture the distribution of molecular energies, with sufficient energy to create activated complex. The proportionate fraction increases with temperature by shifting the distribution of molecular energies rightward. At greater concentration, the curve represents more molecules, but there are more present with both less and more energy than required, so the rate constant doesn't change, though reaction rate, expressed as change in concentration with time does change reflecting the greater amount of reagent, and concentration appears on its own in the rate expression reflecting its effect separate from rate constant.
However, remember you cannot get a rate expression from stoichiometry. Rate expressions have to be empirically determined regarding which reagent concentrations affect rate. This is a top ten favorite MCAT theme. Only if the component is present in the activated complex of the rate determining step will it appear in the rate expression. For example, SN1 and SN2 substitution both have the same reaction stoichiometry, but in SN1 substitution only the substrate concentration appears in the rate expression because carbocation formation is the rate determining step, but in SN2 substitution both the nucleophile and the substrate are present in the rate determining step and both affect reaction rate.
Where the discussion seems to be wandering a bit is to understand the role of a catalyst. It doesn't make sense to say that a catalyst affects rate constant because a catalyst presents a reaction with a completely new reaction mechanism, so you get an entirely new rate expression, or a simple general chemistry rate expression may not be applicable at all. There is a lot of complexity with catalysts, especially enzyme catalysis, and their kinetics because enzyme catalysts may be saturable so there isn't a linear response between reaction rate and concentration. Even in general chemistry because a catalyst is often a different phase, such as the palladium or bentonite catalysts often used, the kinetics are nonhomogeneous which is not chem 101. Complexities aside, if catalysis is homogeneous and nonsaturable you would still have a completely new rate expression with a new rate constant, unrelated to the other, basically, and possibly with different concentration terms, because a catalyst affects reaction rate by presenting a reaction with a new pathway or mechanism.
