That is indeed what the FAQ says, but that being the case, the tool does not actually work very well, and the presentation is incredibly dishonest. The fact is that the JPEGmini versions of these images do lose noticeable quality, but Beamr is hiding this by giving a demo where the images are shown at 25% scale.
Take the dog image, for example. Using the slider, you'd think that JPEGmini nailed it; no visible artifacts whatsoever. But let's look at a section of the image at 100% scale, and see if this tool is really that impressive: http://imgur.com/z12mHnd
...holy block artifacts Batman!