I think the difficulty is in recognizing what is incidental to good research study design and what is a design paradigm at all. Those sites you cite are talking about randomized clinical trials. The research paradigm that is of importance here is the clinical trial part. The randomized part is incidental to the design. That is, any good research will randomize variables that it is not trying to measure so as to "smooth the landscape" so to speak, so that those other variables don't end up being confounding variables. So say you want to design a study that measures the effect of a drug on weight loss. The independent variable here is drug dose and dependent variable is weight loss. Now any good researcher will want to randomize other aspects of the subjects so that they don't become confounding. For instance, you would want to randomize who goes into the placebo group and who goes into the control group so that physician bias doesn't come into play. You might also want to do a double blind here for that reason.
But the point is, these experimental aspects aren't what characterizes the paradigm (i.e. clinical trial) but are rather incidental to it. They are like "red, crispy, tangy, sweet" are to "apple." They describe certain aspects of a particular paradigm but do not characterize it completely. So, in short, to apply a test to see whether something qualifies as a "research design," you should ask yourself if the word(s) itself tells you about the design of the experiment - the point where a competent researcher could do it. So if I said do a randomized study linking drug X with obesity, could you perform that experiment? Most people should say no. Because that doesn't tell you what to randomize, what kind of subjects you have, etc. Similarly, if I said do a double-blind study linking drug X with obesity, that doesn't tell you much about the research design itself. You could go to the lab and do a double-blinded trangenic mouse experimental study or you could go into the clinical and do a double-blinded clinical trial. But if I said "do a clinical trial linking drug X with obesity," then a competent researcher should be able to perform that experiment and he/she would also randomize the appropriate aspects of it too to make it good science.
Overall, a research design should tell you how to collect, measure, and analyze data. It's basically your blueprint for research. "Randomized" tells you how to collect certain types of data. It tells you nothing about how you're going to measure something, where you're going to measure it, or how you're generally going to analyze it.
Of course, others should feel free to weigh in if they can explain this better.
