This is completely wrong. The Safe Harbor provision gives a content site the ability to be safe from infringement if they comply with the specific rules set forth in the DMCA.
The onus is on the content provider first and foremost. They need to remove the material and then notify the provider of the material. If the provider can show it's theirs it can go back up. If they can't, it needs to stay down. If the DMCA notice is completely wrong, the provider of the material can go after the accuser for monetary damages. If Apple doesn't take down infringing material, the are no longer under safe harbor[1].
That said, Apple can do whatever they like with their platform, and show little compunction about doing so.
You were defending Apple for not taking down the offending material say that they don't have to because the DMCA gives them safe harbor, and that's completely untrue. Apple is complicit in the infringement until they take it down 'expeditiously'.
The onus is on the content provider first and foremost. They need to remove the material and then notify the provider of the material. If the provider can show it's theirs it can go back up. If they can't, it needs to stay down. If the DMCA notice is completely wrong, the provider of the material can go after the accuser for monetary damages. If Apple doesn't take down infringing material, the are no longer under safe harbor[1].
[1] http://www.chillingeffects.org/dmca512/faq.cgi#QID130