Although this is generally a true statement, it is not alway true.

In general, people do demand more of a product when it is at a low price and less of it when it is at a high price.

However, it is at least theoretically possible to have a product for which demand is perfectly inelastic.  For such a product, people will buy the same amount regardless of the price.  Here, the demand curve is vertical.

It is also possible for a product to have perfectly elastic demand where people will buy a given product, but only at one price.  Here, the demand curve is horizontal.