It is certainly ture, but also an enormous oversimplification
What is written on the label of the bag is not relevant. What IS relevant is what is inside the bag - the food itself. A great many adult formulas, and all all-life-stages formulas are perfectly well suited to puppies - and in some cases, far more suitable than foods labelled "puppy".
That does not mean grabbing anything with adult on the label and expecting it to be suitable. And it doesn't mean discounting anything labelled for puppies. It means looking beyond the advertising, and selecting something suitable for growth stages, that is neither excessive nor insufficient for a growing pup.
If you prefer to rely solely on the labelling, then an all-life-stages food is the safest option (those foods go through more testing than any restricted life stage as well).