The main problem that we have with Internet usage is that it is ephemeral: it doesn't last. If we cite a printed source, later scholars can in principle go back and check it, but if we cite a word from a website, it may not be there tomorrow.
But the academic community is developing ways of citing Internet sources and we certainly record Internet usage in our files even if we haven't yet found a reliable way of actually quoting it in the dictionary. We also make extensive use of Internet research sources such as electronic versions of journals and encyclopedias, some of which no longer have direct print equivalents: more and more examples in the material added to the OED Online are marked (Electronic Edition).