It simply says that if you want to evaluate all paths from Cambridge to Palo Alto that go through the airport, you only need to consider those that use the quic

It simply says that if you want to evaluate all paths from Cambridge to Palo Alto that go through the airport, you only need to consider those that use the quickest way of getting from Cambridge to the airport, because all others can't be faster than that. This is different from getting stuck in a local minimum, it's merely a dynamic programming approach to reducing the computational burden of finding the global one.