Hi Kate,
I'm a fellow user of Just the Word and I think you just need to explore the site a little more. When you click on the collocation (in blue) you will see the list of actual texts where this collocation occurs. Glancing down the list, it's obvious that give opinion requires an article or possessive adjective. You will also find that 'have in opinion' only occurs in situations like "... a colleague who had, in my opinion, acted irresponsibly" and "If he could have turned them down, he would have, in my opinion."
I don't know exactly how the software works, but I believe the collocations are generated by computer analysis of thousands of texts. They are not human-generated, and therefore it's not realistic to say that the site needs to be tidied up. In fact, your students just need to understand the site a bit better.
With my students I always tell them to click on the blue collocation to look at some examples before they start using the collocations. A classic one was "come on the news". They insisted it was a very strong collocation, and I was very suspicious, until we clicked on the link and found a vast list of "Still to come on the evening news ..." Ooops! Like any mechanised process, a bit of human common sense is required. Do a few examples with your students to train them to use the blue links and the example sentences that are listed to spot any problems or rules. They don't need to read every example sentence or understand very much of them - just spot problems and patterns (article use is a particularly common one).
The site uses the British National Corpus, which is a huge collection of written and spoken texts. I believe the codes at the beginning of the example sentences tell you what kind of text the example comes from - spoken, written, genre, etc. but I haven't really used them.
I have to say that I've always found the "combinations" option works much better than either of the "alternatives" options.
Hope that helps!
Gabrielle