I agree that differences in ball reaction are greatly magnified on tougher patterns (i.e. Sport, USBC Open, etc.). However, I disagree with the claim that a bowler has to use Company X over Company Y in order to get those matchups. Just about every company out there produces quality equipment these days. If you know how to use the proper layout and coverstock prep, you should be able to match up to whatever conditions you face.
Now, that is not to say that certain balls don't make it easier to do so. We all know there are some exceptional balls out there that just seem to match up for just about everyone. Likewise, some people tend to think that they only find those magical matchups when drilling balls from a particular manufacturer. In my humble opinion, that is usually just a matter of confidence. For example, if I've had a lot of success with balls from a particular manufacturer, I may be a bit more confident out of the gate whenever I punch something new from that company. That isn't to say that certain bowler styles won't match up better with certain core and cover combos, but I think the concept is overblown for 99% of the bowling world.