The degrees of unsaturation for a hydrocarbon of formula $\ce{CxHy}$ is equal to $\dfrac{(2x+2-y)}{2}$. The addition of an oxygen atom does not change the number of degrees of unsaturation, so acetone has 1 degree of unsaturation. This is confirmed by looking at acetone's [structure](https://en.wikipedia.org/wiki/Acetone#/media/File:Acetone-2D-skeletal.svg), which contains a double bond between the carbon and the oxygen. Reacting acetone with $\ce{H2}$ will result in 2-propanol according to the reduction reaction found [here](http://chemistry.elmhurst.edu/vchembook/703reduction.html), and thus, 1 mole of hydrogen should be required to convert acetone into a saturated compound. 

While acetone is not a saturated compound, the degree of unsaturation comes from the carbon-oxygen bond. All of the carbon-carbon bonds on the compound are saturated, and that is probably what the teachers who said that this compound was saturated meant. [Here](http://chemwiki.ucdavis.edu/Core/Organic_Chemistry/Hydrocarbons/Alkenes/Properties_of_Alkenes/Degree_of_Unsaturation) is a link to learn more about degrees of unsaturation.