That's exactly right. Or at least inform people on the website and in advance that there will be questioning on arrest records (even when not convicted) and that the applicant should know about these and have documentation or whatever about them.

The larger issue is that the website makes it clear that people are eligible for this program unless they have convictions. It says nothing about arrest records or about being refused entry to a foreign government. It doesn't even convey warnings about this making it difficult. Its misrepresentation.