To me it seems that these statements are needlessly specific. They remain technically truthful if: - The back door was created by a third party. Apple didn't create it. - Apple created a backdoor without working with a government agency. - Apple provides a "frontdoor". Some sort of bulk access to the data that is not considered a "backdoor." - many variations on the same theme.

Same thing with allowing access to their servers. They may provide access to some other part of their infrastructure. The government agency may provide their own servers that are a mirror of Apple's in a way that does not require direct access to Apple's servers. And so on...

Tim Cook should have said something like "We do not provide bulk data to any third party."