I don't know if this is true but I saw in their changelog http://mdlabs.se/sleepcycle/changelog-v3.0.html that they "removed "dreaming" from graph legend we've done a lot of research around this with help from sleep scientists and determined that Sleep Cycle cannot reliably detect when you are in REM sleep".

That makes me think they're legit. Their test function is also pretty convincing. It detects large and small movements quite accurately.

I've been using the app for a couple of months and I feel that I am groggy less often when I wake up (though this could be expectation bias). It seems to work much better when I am sleeping alone I or my partner are traveling, though maybe this just means I need to buy a bigger bed.