This will obviously vary among countries, institutions and also departments.
At my department (a Norwegian University (magic fairyland where "PhD student" is a regular, well-paid job), CS dept.) I did my first lecturing as a PhD student (a Master-level, seminar-style course) and was also the official "instructor" (together with another PhD student). The year after, while still working on my PhD, I was employed to teach a major undergrad course, also as the official (and solely responsible) instructor; I had no supervision or follow-up: no one pre-approved my lession plan, checked on my lectures, looked at the exercises I made or even checked the exam and the grading. Fortunately, it went well, and I was given the course again the next years (as a post doc), and I'm still teaching it now (as associate professor).
On the other hand, at our neighbouring department, they don't even let PhD students and post docs be officially responsible for small stuff like supervising bachelor students.
In general, good teaching requires both skill, knowledge and motivation. If you're lucky, your personality and previous experiences will be enough to do good or even great teaching, even if you're an inexperienced PhD student (or perhaps not even that – I've had 2nd year Bachelor students deliver awesome lectures!). It's quite a gamble, though, and an inexperienced lecturer can just as easily be a disaster (then again, the same goes for an unmotivated experienced one).
So, it makes sense to provide fresh lecturers (whether they're PhD students or newly hired staff) with guidance and supervision until both they and the department are comfortable with them taking full responsibility. Educating and training people is part of a University's mission, and that also applies to training lecturers – a department shouldn't just pick random PhD students to lecture courses and hope they eventually hit on a rare, talented "great teacher".
So who should be the "instructor on record"? The person(s) who's actually responsible for the teaching, no matter the title. Having a rule that says "a PhD student can't be ultimately responsible for a course" is probably meant to avoid having courses taught by underqualified lecturers and sort of makes sense from a bureaucratic perspective (could even be that my own University has more-or-less this rule). Doesn't really help, though, if the department appoints a nominal "official instructor" and gives the actual job to a PhD student anyway.