Exactly. So the answer is false.
By poorly worded, I thought you meant that it was poorly worded.
Sounds to me like it is definitely worded in such a way that YOU understood that it wasn't always true. Just because a true/false question is worded in such a way to make it not true, doesn't make it poorly worded - surely SOME of the questions need to be false, else the test would be too easy.
Now... if the answer key says true, we have a different issue don't we?