The problem is not that academic standards are too strict for the Internet Age. Rather, it’s that students are not taught that such standards really matter.Or, from this teacher's perspective, students aren't always taught why such standards matter. We stop just short, teaching them the correct citation style, and perhaps even telling them that plagiarism is wrong, and that they'll receive a zero for a first-time offense. But that's only a threat without a reason.
Why does plagiarism matter? In this teacher's perspective, the educational reasons come before the ethical.* In a classroom where assessment is at the core of instruction, and I establish and maintain the expectation that I need to know what you know, then the corollary is that plagiarism defeats that purpose. There simply isn't room for it.
It's doubly important for an English teacher; our focus on "papers" should be on the process, not merely the product. If we have an eye on each draft, especially with amazing digital tools like Google Docs, plagiarism should be nipped in the bud. Nearly all of the (very few) incidents I've seen in the past few years involved students who hadn't turned in their drafts on schedule. For them, plagiarism was a desperation move.
*Regardless of the varying ethics practiced by students--they're not all going to be Kantians, after all--the classroom ethos of purposeful learning must be foundational.