No, but I live in a country where we don't have grades (at least not any I know about ...) and we seem to be doing well anyway.
To answer the OP's question, I believe what your friend's teacher meant was that there are some things in certain grades that you only really learn or explore IN that grade. Think of it like skipping a grade in school, for example. If you skip a grade in middle school, it's possible to go straight from pre-algebra to geometry, skipping algebra altogether. This may or may not cause problems depending on the person skipping a grade, someone who is able to skip a grade because they study above their grade level won't have a problem with missing Algebra class, but someone who skips a grade just because they're all-around smart might miss a few concepts which could cause problems down the road.So I imagine that's what your friend's teacher meant, you could miss some core concepts by skipping grades, depending on who you are. But there are plenty of things you won't learn in these types of grading systems that are pertinent to being a musician too, so take it with a grain of salt.