This is severely misguided. If you're Tim Berners Lee, then yes, Google success could be a source of pride, because you enabled the success of this company by inventing the web. If you were one of Larry Page's professor, then maybe you can take some pride in the accomplishments of your student. If you're Sergey Brin's mom, you can be proud of how successful the son you raised has become. But that pride has nothing to do with being "British" "American" or "Russian". It has to do with your personal contribution to Google's success.
At the end of the day, either you've had a measurable contribution to something of value, and you can be proud of that, or you didn't, and you don't get to be proud just because people who have a similar passport to yours have.
You insist on using the word "pride", which Rayiner didn't. If you'd like, I'll stipulate that ordinary Americans shouldn't feel "proud" of Google, so that we can move back to the actual discussion of whether Americans should "take a little credit for" Google.
The discussion was started by Tepix which referred to pride. And no, merely being American does not give you credit for Google. For most people, it's very hard to know if they've made the environment better or worse for Google.
At the end of the day, either you've had a measurable contribution to something of value, and you can be proud of that, or you didn't, and you don't get to be proud just because people who have a similar passport to yours have.