Surveys are hard.
Rather than "Are you aware that Google does X?" (which implies that Google does x implicitly) to something like "True/False: Google does X"
Transparency is at the center of the argument of the morality of surveillance. There is nothing inherently immoral about collecting data from a consenting party, but it's impossible to gain consent from consumers who don't even know that they're under surveillance.
If you are attempting to test peoples existing knowledge of a situation, you don't want to offer new information before you gauge their existing knowledge.
But this is a difficult question as well. Speaking for myself, I cannot say that I am aware of what Google is doing with my data. I fully expect them to use my data for any and all purposes they can think of, and I'm not okay with any of that -- but I'm still not aware of what they're actually doing.
I'm not sure that's true. From the article itself: "DCN surveyed a nationally representative sample to find out what people expect from Google — and, as with a similar study we conducted last year about Facebook, the results were unsettling." Since the notion of "expect" is baked into the purpose, I think some manner of "okay with it" is fundamental to the survey. (Because when people don't expect something, that's usually not okay.)