Well, my point here is risking the part that the officer may doubt about the genuiness of her relationship to her husband. Because ex is ex, past relationship is already past, meaning no more commitment or responsibility to each other, but if the ex is still depending on his/her ex, then it could raised a redflag. For example, The husband will write down his ex-wife's name under dependant, and what will be the relationship to the PA he will put in there? Ex wife? Ahhm not good. And also, its not lying, he will just declaring it in different way. Instead of financially supporting the ex-wife and their children, he can just say co-parenting with his ex wife and financially supporting the children. Because they are already legally separated which means the husband doesnt have any more responsibilities to his ex-wife, and it is automatically means that the ex-wife should support herself and not depending on his ex-husband.
Its like, sugar coating it. You're not lying, but you're just declaring it in more safer way.