You are ranting about one particular word in one particular language.
However, in all languages (not just English) many, many words (verbs, adjectives, nouns, whatever) are used by native speakers in a way that may differ from how non-native speakers have been taught those words in a classroom.
In colloquial English, we often say "do your research".
This expression doesn't mean "please go away and conduct several months of scholarly investigation."
Rather, it means "I advise you to go and find out some information about the topic you are talking to me about."
In addition, I have to correct you on your (mis)understanding of these two verbs. "To look up" and "to research" do not mean the same thing.
"To look up" is a very quick process. It refers to searching for one word or expression only. Once you have found that particular thing, the process of looking it up is finished. Therefore, looking something up on the Internet takes mere seconds (just like looking up a word in the dictionary only takes seconds).
In contrast, researching something on the Internet means reading many articles about it. Researching something online could take hours, days, or weeks. I often spend time researching things online and it takes me a long time. Research involves a lot of reading.
By the way, "copying the relevant sections off the Wikipedia page" wouldn't be research. That would be plagiarism.