Everybody involved in this (serious) game knows that people can have multiple passports and that the ones with disadvantageous information are usually not shown

Everybody involved in this (serious) game knows that people can have multiple passports and that the ones with disadvantageous information are usually not shown. There is indeed an ongoing risk that authorities get information some way or another (flight records, informants, data breaches, social networks) and start connecting dots. Intelligence services probably do that all the time to keep tabs on operatives of other countries. In the Iran case, the safe way seems to disclose the double citizenship and accept the babysitters. As a Swiss, I would clarify with the Swiss embassy whether they can intervene in case the double citizenship causes further problems. It seems likely, as the person would still be a Swiss citizen. It all depends how much hassle it is to sour the diplomatic relationship with Switzerland.