Well if they had an approved guide cannot see why they were arrested, fir even though Iran is a dangerous country to travel to people do travel there with guides. The thing is that on the news it said the couple were working on a psychology project asking people in every country about the society/country they lived in. My guess is that someone reported them for interviewing people - and they presumably recorded it - without asking for approval from the authorities first, especially if they were asking them about their experiences of living in Iran.
We travelled to Iran many moons ago, we didn’t need a guide back then and had friends we knew living there, is an amazing country, one of the most breathtakingly beautiful we have visited, and have traveled to many parts of the ME, also the people are extremely hospitable.