"They're either parsing the query out of the url, or violating robots.txt to fetch the result page, almost certainly the former."

Where's your evidence for any of that?

There's another way. Store the input of any Text Box which is immediately followed by a form submit,(search term), and then store the href of the subsequent click (the result which the user finds helpful).

The above is a way of handling it (naive and abstract) which doesn't target Google, and in fact would work for insite searches as well, or any search engine.

Since you've already made up your mind that your two ways were the only way of doing things, what's your opinion given the above?