I think the response was rude. If the person didn't want their partner to open their mail they could have simply said that they'd open when they got home. No need to accuse their partner of being nosey.
My DP works away so I have to open his mail in case it's something that need actioning before he gets home (usually a bill to be paid!). I always ask him first (and send him a photo of the envelope/package) if it's the lead up to Xmas or my birthday. He often shops online for my presents.
Earlier on in our relationship I'd just tell him that mail arrived and send him a pic of it all (unopened). That way the ball was in his court. He'd always ask me to open it but I wanted him to have the option of privacy, particularly as he was going through a divorce and I knew some of the mail was divorce related.