Let me paraphrase your post to confirm we're talking about the same thing. You observed that in ELU, the people who answer typically have a firmer grasp of English than the person who asked the question (the OP). You're then asking why it makes sense for the OP to judge an answer.
It makes sense because the OP is the one who needs to be satisfied with the answer (see Andrew Leach's answer). The question remains: without knowing the answer beforehand, how should the OP decide when a question receives multiple answers and the answers don't agree, other than looking at the tally of votes?
They decide by looking at the support provided for each conclusion. ELU answers should be supported by appropriate justification such as dictionary definitions, logical argument, statistics, usage example and so on. These lend credibility to the answer; conversely, their absence can leave an answer looking weak. (See, for example, my answer to a related question).
ELU regulars also tend to point out flaws in answers rather freely, subject to the be nice policy. Although criticism is on occasion unwarranted, the discussions tend to bring out nuances of questions and answers that may have otherwise been left unaddressed. The process tends to validate or to invalidate an answer more clearly than just the bare answer. These discussions can provide valuable information to the OP regarding the correctness or otherwise of an answer. The answers themselves are often improved upon as a result of these discussions.
Note that all this also influences the community's votes on answers, which the OP can use as a gauge of each answer's popularity.
In short, the community's involvement and our preference for supported answers help the OP to judge the answers they receive. Based on this informed opinion, it then makes sense for the OP to award the green tick to whichever answer is most helpful.