> Apple very heavily relies on the claim that they have no such back door

And, at least in the case of their private cloud compute, they encourage third party audit of their claims and even provide a virtual research environment running an instance of their PCC on your mac.

The UK explicitly requesting a backdoor to iCloud's advanced data protection forcing Apple to pull the service instead also tells me their claims are legit.

It's certainly possible a backdoor exists in hardware instead, or elsewhere in the stack but given Apple's surprising relative openness for how they implement their privacy products & the research papers they put out I'm inclined to believe them for now. (I say relative because its not open source, which is the only way to be 100% certain, but their research papers are surprisingly in depth).