In digging a little closer to this story, I have found reports that Prince William went absolutely nuts over this silly prank. He was demanding an investigation of the hospital. So perhaps in the end, it was the Royal Family - once again - behaving badly.
I have not followed this story but it sounds like you are correct.
Where did you read that? I read the DailyMail every day, and DM said William and Kate were not the source of complaints, and were greatly saddened by the woman's death. Citation?
William and Kate 'deeply saddened' by death and said they did not complain
Even if William had complained, which he denied, one couldn't blame him for being vigilant about his ill wife and threats from the highly intrusive media, given what happened to his mother. The UK and Murdoch pretty much invented the mainstreaming of tabloid journalism.