The authors did not do any work to establish it as a reasonable proxy. We know that's the case, because they don't describe any of that work in the paper. they just state that they're using this proxy measure, and then seem to be using Startpage and Google interchangably for the rest of the paper. Sure, if they'd actually done the searches on Google, the title would not be outright dishonest. But they didn't, so this defense of yours is just absurd.
It's pretty obvious why the results won't be the same: the feature sets of the search engines are different despite being based on the same index. Startpage's own documentation even has a page on how and why the results are different!
(Personalization is a part of the Google feature set, and has to be taken into account when considering the results. It's also a part of the Bing feature set. This didn't stop them from reporting the results of their testing on Bing in detail.)
It's pretty obvious why the results won't be the same: the feature sets of the search engines are different despite being based on the same index. Startpage's own documentation even has a page on how and why the results are different!
(Personalization is a part of the Google feature set, and has to be taken into account when considering the results. It's also a part of the Bing feature set. This didn't stop them from reporting the results of their testing on Bing in detail.)