No? Because for me it is simple.

The cheater lies and deceives. They might claim that they are working while being with a lover. They'll do things on their partner's back. Use money from the common budget to woo their lover and can't be reached for the periods of time they are with their lovers.

The non-monogamous couple knows when their partners are with a lover. Since there is no need to lie, they also know how much their partner is spending. And if there is an emergency, they know where their partner is and how to reach them.

In case of an accident, the cheated-on person might add not finding their partner to the stress of the situation. The person in an open marriage would only interrupt a date.

If you can't see the difference it is on you. But for me is as simple as doubting your partner's word or knowing that they'll be honest.