Does it "really" matter if the sites you use are credible or not? Are there times that you will want to use a certain standard of crediblity to be able to "prove" your point and are there times that you really don't care how credible the information you use might be?
You have to be kidding, asking if there are times that you don't really care how credible the information is. Why don't you just visit a local elementary school and ask a class of first graders?
I cannot imagine not worrying about the credibility of sources.