Yes, it is true. However, the problem is not with the coffee itself. It is the milk and sugar in the coffee which can be metabolised by bacteria in your mouth into acid.The acid causes the outside layer of enamel (hard white material on the outside of the tooth) to demineralise (soften) temporarily.
If you brush your teeth during this period you may brush away the top layer of enamel.If you leave the brushing for at least 30 minutes, the enamel rehardens itself as your saliva buffers the acid in your mouth. Alternatively you could rinse with water after finishing the coffee to dilute the acid and rub some fluoride toothpaste against your teeth with your finger tip. Food and drinks which are acidic, including most soft drinks, fruit juices and sports drinks have this effect on your teeth. It is best if you brush your teeth with fluoride toothpaste first thing in the morning and last thing at night.