Part of the issue is that many people will be willing to answer questions like these anonymously, but asking the "why" identifies those employees. Most of the time people don't speak up because they are afraid of the consequences/ramifications.
This is a great point. If you can at least discover that there is a problem, you can find some other means to uncover and solve it.
to be fair, since the probability of the employees answering yes is already really high, you could just assume that the answer is yes, and then do that investigation.