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No puzzle here. You can only log in if Google has flagged your search topics.

On google search, you have the variable window.location.search = "?gfe_rd=cr&ei=XXXGyZiVNHoFcuF8Qe7wYHACw&gws_rd=ssl"

That string is appended to the url of the iframe: src="https://foobar.withgoogle.com/"+window.location.search

I don't see any mechanism that appends it from any search topics when you load https://www.google.com/foobar/

The code snippet will only load the URL with appended values if there are present in the parent URL: e.g. https://www.google.com/foobar/?some_query_string

That's why the link to foobar turns up in people's search results.

Ah! Do you mean the 'chosen ones' will get search results linking to https://www.google.com/foobar/ with a special query string?