Turing completeness means there's nigh infinite ways to convolute malware that will evade all scanners. And as long as users have capabilities to their data, they will be subject to attacks against data they have access to.
Tl;dr. Grandiose claims require grandiose proof.
No, it does not. Turing-completeness simply means that for certain properties which could be true or false about some software (like whether it halts), given an arbitrary piece of software, you won't always know whether or not it satisfies the property. It does not prevent you from assuming "No" in the cases where you don't know. Nor does it prevent there from being other properties (e.g., ability to access another user's data) for which the answer is always no.
What you typed is good for an academic setting, in the "wellactually technical correct" sense of the term.