No, I do not agree with this statement. There are some important cases in which the demand for the commodity is greater when price rises and smaller when price falls. Such cases are called exceptions to the law of Demand. In such case, demand curve slopes upwards from left to right and it has a positive slope.
- Prestige Goods : Rich people buy more expensive goods like gold, diamonds, etc., even when there prices are high to maintain their status.
- Giffen Paradox : Demand for low quality goods and inferior goods decrease even if there prices falls. According to Sir Robert Giffen when price of bread declined, people did not buy more because of increase in their real income and they prefer to buy superior goods like meat.
- Speculation : People are tend to buy more commodities if they expect prices to rise further. E.g. prices of oil, sugar. etc., are expected to rise before Diwali, so people buy more of these commodities even at higher price.
- Habitual goods : Due to habit of consumption, certain goods like tea is purchased in required quantities even at higher price.
- Ignorance : Sometimes people completely ignore the price of commodity and buy more of that commodity ignoring higher price.
- Price Illusion : Consumer feels that good at higher price are of better quality, therefore demand for such goods are higher even at rise in their prices.
