Right on.
I have a DSLR, and even with my 50mm 1.8 lens at ISO 1600 for the fastest shutter without too much noise, I cannot get crisp pics of moving subjects in low light without flash. It's just the laws of physics. The faster the subject is moving, the faster the shutter speed you require for a visibly sharp shot. There is no way to get a bright exposure at 1/500th or faster in low light without super high iso or an F0.5 lens which doesn't exist. That's where a 5000 dollar full frame DSLR shot at ISO 12k with an F1.4 lens would come in handy
I've had an iphone, 3 blackberries and several androids, this note 4 really is the best IMO. The things a camera does do that affects a photo, this does great. It's white balance is really close most of the time, it balances it's flash the best I've seen, you can use it when closer to the subject without over exposure which most phones suffer from. It's HDR is great (my HTC ONE has horrid HDR, you have preset exposure, then switch to HDR for every shot otherwise it blows out the highlights like mad).