Is it true that Koalas are unable to eat anything but Eucalyptus leaves?

Its true. Stomachs have adapted so can only digest the eucalyptus. Same as pandas and bamboo - except for the stripes.

Koalas eat only eucalyptus. There are about 200 kinds of eucalyptus found in the world, but Koalas eat only about 12 kinds. They are herbivores, which means that they will only eat plants and vegetables. A bowl of lettuce and tomatoes would not appeal to a Koala, being they are very picky eaters. Koalas spend about 5 hours out of their day eating so they don't starve. During these 5 hours, they eat up to 2 pounds of eucalyptus. They are able to do this because of their very long intestine. Koalas cannot gain weight.(?) The gum leaves they eat have no fat and are very low in vitamins. It is a poor diet so they have little energy to travel. The word 'Koala' means 'no drink' which makes sense because the Koala does not drink water. Their water supply comes from the eucalyptus leaves they eat.

The koala gets it's name from an ancient Aboriginal word meaning "no drink" because it receives over 90% of it's hydration from the Eucalyptus leaves (also known as gum leaves) it eats, and only drinks when ill or times when there is not enough moisture in the leaves. ie during droughts etc.
Koalas like a change, too, and sometimes they will eat from other trees such as wattle or tea tree.
http://www.thekoala.com/koala/

They don't drink either, and "eucalptus" are the leaves of eucalyptus gum trees, and only specific ones at that.

They don't only eat the leaves of the eucalyptus tree but they spend their money on Wrigley's gum

While koalas eat mostly eucalyptus leaves, their diet is not limited to them, nor are they unable to eat anything else: https://en.wikipedia.org/wiki/Koala#Ecology_and_behaviour

They prefer specific eucalyptus leaves but will also eat others such as tea tree, wattle or paperbark.

https://www.savethekoala.com/about-koalas/koalas-diet-digestion