On Tuesday, Sue's mother died. I only know this because a mutual friend, Cathy, was going to go visit her and Sue texted her to say her mother had died. Cathy told me, but told me not to say anything because it was Sue's news to share, not Cathy's. I agreed and said nothing.
I find that reasoning bizarre. That might go for other personal news, but like others have pointed out, deaths are public. Death notices are published in many local papers. There is no reason to keep that stuff secret.
Definitely call her and offer your condolences. If you are interested in attending the viewing/visitation or funeral, start asking around.