Well - the fact ARE correct! We are extremely simlar, according to our DNA. However, we have to straighten things up a bit, because we can not just count the number of similarities.
Basically: 1 similarity can be big, or small. So its just not the amount of similarities, it's also about the impact of the similarity. So even if a humans DNA is 96% similar to a chimpanzee, it does NOT mean that we are 96% similar over all.
The base for all lives is oxygen. Both a chimpanzee, a banana and a human needs oxygen to live. That is stored in the DNA. So it is not that strange that we share so much of the DNA with other species among our planet.
A better explanation that we can provide can be found here at HowStuffWorks.