I don't pay much heed to the argument that there is no guarantee that Googled answers are right, simply because there is no guarantee that any answer, Googled or otherwise, is right. Incorrect answers that receive upvotes are a problem, but I don't think Google is the cause.
As far as the specific example of copying content and GameFAQs in particular, my experience as a reader and contributor to GameFAQs is exactly the opposite... most authors don't mind if you copy their work so long as you aren't trying to make money off it. And most FAQs I've read have specifically stated if someone had a problem with it. But that specific example aside, I don't know enough about this issue to know if legally it's a real problem or not.
When it comes to answer rot, every answer risks suffering from answer rot. Googling aside, does this mean I shouldn't leave an answer on the site if I don't think I'll be around a month, year, or decade from now to correct it myself? Am I responsible for maintaining and updating every answer I leave, for all of time? There are already tools in place to combat this problem.
If someone literally knows nothing about the game and slaps the first thing they find on Google as an answer, then yes, that can be a problem, particularly if what they cut & paste looks good, which will tend to give it upvotes, correct or not. But how often is this really the case? I've answered quitequite aa fewfew SWTOR questionsquestions that were a combination of my personal experience with the game along with researched (a.k.a., Googled) knowledge. So I think this is definitely a problem if the answerer doesn't have enough experience to even know if the answer is correct or not, but again, that's what downvotes are for. What other alternative do we have? Reject correct answers because we don't like their source?.
For me, the issue really comes down to whether or not the answer is correct and well-written, not where it came from. The community has tools in place to deal with out of date answers and incorrect answers, regardless of their source. And lastly, if SE has a policy against Googled answers, how exactly does one police that? Short of an extremely obvious cut & paste job, there's no way to know whether an answer was Googled or not.