I suspect this professor is one of those people with an axe to grind against Wikipedia and other resources for not being trustworthy enough. Problem is, these kind of tactics would apply to old-fashioned print publications just as well. In the end it all comes down to a matter of trust: the reader has to trust a publication, the publisher has to trust an author, &c. Teaching people to violate that trust can only do harm. His exercises are probably more exciting and sensational this way, but if you ask me it would be more constructive & useful if he asked students to track down and correct surprising inaccuracies for example.
You're setting up a false dichotomy. You seem to feel that either the Internet is a place that is 100% trust-worthy (so much so that you can take off your critical-thinking cap), or it's a place where everything is a lie. The point here is that people should learn that they can't blindly believe things just because they read it on the web, not that lies on the web will render it completely useless.
Your problem is that people might start to mistrust things they read on the internet? That's surely the opposite of a problem.