Obviously Nadia shouldn't have had an affair, and (surprise surprise!) she seems to fail to mention that when talking about him, but I think I can sort of understand where N could be coming from.
For him to take his own life as a result of infidelity is an extreme (and heartbreakingly tragic) reaction. As with anyone who commits suicide, there must have been deep issues within his psyche: it is such a sad and avoidable way for anyone to go.
I can't pretend to know the specifics, but I can imagine a situation where someone wouldn't want the note or the ring. It must be very difficult as the (separateds) spouse to know that your husband is in such a bad place that they a) commit suicide and b) potentially try to use it as leverage against you, and impart feelings of guilt onto you.
I can see why someone wouldn't want to read the note, or to collect the rings. It can be a way of control and emotional manipulation from beyond the grave by someone who was in the midst of a mental health crisis. I'm sure his family talking to the press and leaking very delicate, pointed and private signs to her in his last minutes of life, while trying to insinuate blame, also probably didn't help.
Obviously it depends on the contents of the note, and I obviously don't know the specifics, but I'm not sure I would want the note or the rings, but I also see how that can look quite heartless from the outside.