No. The only people who make this claim are Apple critics who put words in Apple's mouth to justify whatever clickbait blog post they're putting out this week to pad their resumes and harvest echo chamber thumbs.
But as we know from politics, if you tell a lie enough times it becomes the truth.
In the article you linked to, I didn't see Apple claiming they alone can protect user's privacy. I read instead that Apple suggested all companies should strive to protect their user's privacy.
Not seeing Apple claiming only they can protect user's privacy. Instead the article quotes Tim Cook trying to pressure the governments t recognize privacy as a fundamental human right.
But as we know from politics, if you tell a lie enough times it becomes the truth.