There is a paradox here. Implication IS tricky. Part of the reason is it's REALLY HARD to avoid implicit assumptions in human scenarios. The only absolute way to avoid assumptions is to translate the English into meaningless symbols (p, q) and rigorously apply logic rules. The rules themselves are tricky. You pretty much need to prove them once to know they are correct, then apply them by rote from then on. Your example is on the cusp what most people can handle in their head. For anything much more complex, most of us will need to manipulate symbols using logical rules to "reason correctly."
In your example, some of your students will intuitively see the correct premise and conclusion. Others will need some help. All of us will need some help if the scenario gets complicated enough. (Or if it is sneaky enough to trick us into making unwarranted assumptions. It happens.) I'll probably lose points for politicizing this, but consider the recent debate on gay marriage. There were some not irrational arguments along the line of "If you want to have children, then you should be married." But there was an implicit assumption of bi-implication. Not once did I hear anyone--on either side of the debate--point out that this is not the same thing as saying "If you want to get married, then you should have children." So this sort of logical error is very easy to make, every by well-trained people.
I agree with Daniel and his blogs. The only solution is formal training in logic. If only to make people aware of how EASY it is to make mistakes.
If you're looking for the most bang for your teaching buck, what I have personally found the most useful is this:
What implication is: An if-then statement. Show how to identify the premise and the conclusion.
Show the differences between the INVERSE, CONVERSE, and CONTRAPOSITIVE. My first exposure to these three conditionals was a real eye-opener. It did more than anything else in my life to avoid the kind of error shown in your example.