Second, Google cannot access all Ajax elements- at least not Ajax enabled textbox(s) like what Google uses for search. In fact, they describe how to make Ajax elements crawlable here: https://developers.google.com/webmasters/ajax-crawling/. Google cannot and will not enter values into an Ajax enabled textbox searching for stuff. They actually say so. The scope of Google Ajax is well defined and began with Facebook and Disqus for comments. http://www.seroundtable.com/google-ajax-indexing-14241.html
To be clear, so far Google is not abusing websites and you have nothing to worry about. It is not indexing elements that you would not want indexed. However, if you want Google and others, BTW- Bing does this too, from accessing these elements, then Google recommends putting in specific lines to each element/resource in your robots.txt file as normal. You can read the recommendation about half way down this page: http://googlewebmastercentral.blogspot.com/2011/11/get-post-and-safely-surfacing-more-of.html.