How could your ISP possibly be a third party network? You're a directly attached user on the ISP network, within their management and addressing domain. The network exists explicitly to move your bits, and you're paying for the service. A third party network is one moving bits between stations that aren't part of that network.
If you ran a big network that Google needed to transit through to get to stations beyond your network, then yes, there'd be a transit settlement in place. That's how the Internet works. If you ran a big network, and your direct users requested access to Google resources, then no, Google would not pay you to deliver the traffic that your users request. You're soliciting the traffic on behalf of your customers, who pay you to do so. There's no reason why Google should pay you their money, and use their resources to fulfill a request that your users are paying you to facilitate.
If you really were to argue that Google should pay, then where do you mark the line? How much traffic warrants payment? Who has to pay? How big do you have to be? The entire Internet would become analogous to people subscribing for PSTN service and then placing collect calls to everyone they want to talk to.