As far as keitai and emails are concerned I clearly have to side with your wife. Emails, letters and cell phone messages are private, and that includes spouses and relatives. I would not even think of touching my wife's keitai and consider it a clear breach of privacy and etiquette if someone touched mine.
As for public baths and onsen: I think that depends on your upbringing. I went to spas and saunas since my early childhood and preferred to go naked if it was publicly acceptable. :)
@ hospitals & doctors: I went to hospital twice in Japan and was always able to consult with the doctor privately. I would also view it a s a clear infringement in medical privacy if other patients would be able to overhear our conversation.
Ergo: I agree, privacy depends on culture and in particular on primary socialisation.