OOhhhh big red flags all over the place.
The wife "proved" that there would be no jealousy? And how, pray tell, did she do that?
Look, it's human nature to be jealous. My husband loves me and is perfectly ok with my seeing other men and developing a relationship with other men, but he still gets a bit jealous. We talk about it and resolve it. I am perfectly ok with the fact that my other guy was married but I was still envious of the time he spent with her that he wasn't with me. There is no way anyone can "prove" that there won't be jealous issues becuase, quite frankly anyone who says they don't have a twinge of jealousy is flat out lying. It's human nature and its' going to happen - especially the first time another partner comes onto the scene. People who understand that and say that they'll deal with any jealousy issues that come up in a reasonable manner and communicate about them - that's healthy. But there's no way she can "prove" to him that there won't be issues.
So now you've got a guy who doesn't "approve" ... but has been somehow convinced by his wife through some "proof" that there won't be jealousy?
Yeaaaah. This has train wreck written all over it.
If you have any interest, I'd ask them straight out exactly what "proof" was provided that jealousy wouldn't exist and if he is actually interested in this or just being coerced by his partner.
And then I'd pretty much say "no thanks" and move on to a healthier dynamic.
That's just me and my take. Others may see it differently.