I'll try to explain Wild's argument in a different way (Wild, please correct me if I'm wrong):
For the sake of argument, we'll presume that there is a Constitutional right to privacy ("the right"). Now we have to decide whether the right applies to your communications with Google.
My limited understanding of how the Internet works is as follows: you use your computer to send information (like a search request to Google). You send the information, which is routed to one place, and then routed to another place, and then to several others, until it finally is received by Google. [I told you my knowledge was limited!!!] If this is correct, your communication has been received by several different sources. Just so, it is difficult to argue that the right was violated after several different sources received and had access to the information you are claiming is private. After all, if you really wanted to keep the information private, you wouldn't have allowed so many others to have access to it. Sort of analogous to using Jack a send a message, who provides it to Mary, who provides it to Jim, who finally relays it to Buffy. You couldn't reasonably expect to keep the information between only you and Buffy after you provided it to so many other people; those who intend to keep information private generally don't expose it to several people -- they release it only to the person who they specifically want to receive it. Now, once again, if I'm wrong about how the Internet works, please forgive me.
The rules of discovery allow liberal access to information, including information possessed by third parties. Basically, any information that could be reasonably expected to lead to relevant information is discoverable. Now, if a third party (like Google) is concerned about the information that a litigant wants, it can request a Protective Order, and ask the Judge to review the information first, or for permission to redact information (like IP addresses), and/or to limit what kind of information the third-party has to provide.
If Google provides the search requests, but does not have to identify IP addresses and/or other information that would identify who specifically made the search request, then none of us Google users can complain. After all, the Government won't know who made the search request; the Government will only know the specific information requested.
Hope this helps; this legal and internet tech stuff is tough!!! maybe I've just mucked things up even more.