The non-public API refers to Apple API methods that are not documented and offered to the programmer.
Apple does not guarantee that this part of the API will work in future upgrades. They can freely change this part.
They forbid usage, so that your app won't break in iOS updates, and so protect your future users/buyers of your app!
The webservice is external, hence does not fall under non-public. This part you need to guarantee, not Apple.