[effable]

Do you think the results would be different if people were asked "If A implies B then does not B imply not A"?

This could just be about using the right prompt - I do not know how information is stored in the brain and whether most people would be able to access the correct answer: "not B implies not A" if the prompt were just "what can we say about not A and not B".

Assuming that most people would actually know the answer if prompted the right way, one reason the prompt given in the article may not lead them to the answer could be that most people do not need to apply Modus Tollens outside of a class on Logic. And thus, since the concept has never been widely applied, at least in their heads, it is not accessible?

This is all conjecture of course.

[falseprofit]

I think this is applied all the time, but we might not always realize when we're using it. Also, while your version of the prompt may be more likely to elicit the correct response, this does not mean the original prompt was somehow wrong.