One sales pitch that you may hear is the "system" one-that skis and bindings from the same company work together better than pairing different brands. We can't say for sure if this is true, but we can't refute it absolutely, either. Here's why: The skiers who slope tested Company R's skis almost certainly used Company R's bindings (if Company R makes bindings). The testers then told Company R's engineers what they thought, and changes were made to the skis based on the input. The "system," therefore, was fine-tuned and presumably made better. Unfortunately, there are other factors that had equal or greater influence on how the skis performed, like the size of the testers' boots and what boots they were using.
So, will another brand of binding make the ski perform differently? Almost certainly. It might ski worse, but it might ski better. We've tested systems in the past, using the recommended setup from a company and then tried the same ski again with a different company's binding-with everything else remaining constant. There was no consensus among our testers as to which setup was best, confirming that binding choice is but one of several factors that can influence a ski's performance.