The “nearly impossible” statement is correct. That doesn’t mean it doesn’t ever happen, it’s just extremely unlikely, especially on fully updated iPhones. You’ll see Apple release announcements and update patch notes semi-frequently that include fixes for zero-day vulnerabilities. But these are zero days used by nation state actors and NGOs, not 1st year IT students.

A national security job in the US? No, they aren’t going through your phone or web history as part of the background check. They may check your public social media.