"Ignorance is no excuse."
I believe the phrase is "Ignorance of the law is no excuse." It means that if you willfully commit an act, and that act happens to be illegal, then you are criminally liable even if you didn't know the act in question is illegal. That is to say, you don't have to have to form an intent to break the law, you merely have to form an intent (and act on that intent) to commit some action, and that action has to be illegal.
What's at issue here isn't ignorance of the law, but ignorance of the facts, and that, oftentimes, is an excuse. Although possession of child pornography is illegal in most jurisdictions, almost all the statues generally say something along the lines of "it is unlawful to knowingly possess...". There is a very practical reason for this: absent the word "knowingly", anyone could simply e-mail anyone else some images that are illegal, and the recipient could be criminally liable for possession even if they hit the delete key immediately upon seeing it. Defendants could e-mail such images to prosecutors and judges and said prosecutors and judges would be guilty of the same crime the defendant is accused of.
So it is very relevant here whether or not the owners, administrators, or employees of the data storage service knew that they were storing child pornography.