Statistics is not (just) opinion polling, there's a lot more to it than estimating observable properties of a population.
If you're trying to make decisions, predictions or estimates which involve any uncertainty at all (and in my experience big data almost always is), then it's definitely within the purview of statistics even if you have data for the whole population.
Sources of uncertainty include trying to say anything at all about the future (do you have data on the future population? no didn't think so...), trying to make predictions which generalise to new data in general, trying to uncover underlying trends or patterns behind the data you see which aren't directly or fully observed.
Often people expect big data to be able to answer big numbers of questions, estimate big numbers of quantities, or fit big, powerful predictive models with lots of parameters. In these cases statistics can be particularly important to avoid reporting false positives and to make sure you can quantify how certain you are about your results and your predictions. (Amongst other reasons).
