Of course your statement is correct, but it's the word "IF" that matters. It's unlikely anyone in the civilized world eats a truly balanced diet. The problem is that we may think we're eating a balanced diet but we really aren't. And there are other issues as well; such as absorbency problems that diet, balanced or not, will not cure. An example is B12 that isn't absorbed easily by the aged from either diet or ingested supplements. Sublingual B12 is needed, regardless of diet.
One should not simply assume they're eating a balanced diet and forego supplements IF there are symptoms of nutritional deficiency. On the other hand, one should not turn to supplements if their needs can be met with food.
Other aspects of lifestyle matter as well, regardless of diet. One may eat a perfectly balanced diet but stay indoors out of the sun most of the time. That person's balanced diet isn't going to provide optimal vitamin D levels. Vitamin A probably will suffer as well.
One may eat a balanced diet, get sunshine, but be sedentary. That person will likely have hormonal issues from their lack of movement. A supplement won't cure that, but neither will their balanced diet.
One may eat a balanced diet, get plenty of sunshine and exercise faithfully, but stay up until midnight in front of a computer or TV. They are likely to have sleep issues eventually and need a melatonin supplement.
Do we or don't we supplement? We have to learn what's going on in ourselves and what needs we have, individually. We also need to know how our whole lifestyle contributes to our experience.