A couple of points to add
1. From my understanding, the risk of disease transmission and pregnancy is significantly lower from precut than full ejaculation. Therefore, the rule of bareback but no cumming inside may not be totally nuts ( I don't think it is a great idea, but it is not rediculous.
2. On the issue of whether you should be upset, I think you really need to unpack why you are upset. In my mind, the fact that he came inside your wife and the fact that she may have lied about it are pretty minor transgressions. If you allow someone to go bareback while DPing people can get carried away and accidents happen. As for her lie, I would give her the benefit of the doubt - if she was not sure whether he came or not (and I bet she was unsure given she was already full of your gunk and had likely cum a few times herself, it is likely she suspended disbelief a little and convinced herself he did not cum inside her. In my experience, when you are in the heat of a super hot sexual experience, the events blur a bit and recollect is imperfect. So, if you buy my argument that what she did is actually kind of minor, I think you need to figure out why it has upset you so. This is likely more complex