It depends on the alloy, temper and construction, and the location of the damage.
Modern handlebars are often built of loss forgiving alloys (like 6061 or 7000 series) and these can be prone to breakage at scratches or notches. The earlier stuff could be ridden post crash with no worries. OTOH the older stuff was heavier.
Also, deepen than just cosmetic scratches near the stem are of greater concern than similar scratches would be farther outboard. This is because of any lever is always more likely to fail near the fulcrum. (A physics lesson children learn at an early age if they live in cities where seesaws are made of wood.
Other than a legitimate concern about potential breakage, expect to see more stickers like this on everything as the first line of defense manufacturers erect against lawsuits.
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