I tend to disagree, but not with the entirety of what you say. Internet research, simply by merit of it's speed, accessibility and ease of searching, is an excellent place to start.
The dangers of gullibility do not only affect the internet, however, there are plenty of publications, one is listed in this very thread, which appear to rely on flawed research, abuse of information and plain fiction, thusly one must learn to sort the information wheat from the disinformation chaff in print as in pixel. Just as anyone may 'start a website' so they may 'start a magazine' and publish anything they choose.
I agree entirely that only a fool believes everything written on Wikipedia. However, the OED and Britannica are also online - are we similarly to disbelieve everything therein? Of course not.
It is not the medium which is at fault, nor is it the merit of being editable by the general public, who are just people the same as those who publish dusty tomes. It is the error of wooly, complacent thinking which allows one corroborating source to manufacture a 'fact'. All research should be checked and cross referenced with as many different sources as is practicable, regardless of publishing medium. If it is not, then it fails to be research and is no more worthy than "some bloke down the pub told me..."
One advantage of electronic media over paper, as HillBill recently discovered, is when complete cobblers is discovered masquerading as fact on Wikipedia it can be removed staggeringly quickly - in between posts in some cases. Not only does this restore a measure of credence to it , it can also illuminate with great clarity those who will rely blindly upon it.