There is an error in the paraphrasing, Sergey Brin is not calling for all politicians to abandon their political parties. He is suggesting the "victors" to withdraw from their party affiliation while they are governing. There is a big difference.
I think you are correct. Many people seem to not be bothering what he wrote. That being said, I don't really understand this post at all. He recognizes and dislikes the game mechanics involved in political brinkmanship, and then thinks somehow there is any competitive human endeavor that does not involve one? Why not use mathematics to find a better mechanic more suitable to a goal? For example, absolute or adaptive term limits.
Simply renouncing party affiliation leads to Bloomberg style manipulation of the electorate's party affiliations. Some people (most) prefer that the actions and abuses of one elected official will most likely reflect on the entire party in the next cycle. Complicated.
Here is his original post,
https://plus.google.com/u/0/+SergeyBrin/posts/B9VnJXd6Rir