You know how small-sensor compact cameras do not allow narrow depth of field (DOF)? That is why you have a DSLR! On a small camera, everything is in focus and you cannot blur backgrounds.
The “but” is that small cameras also allow very close images to be taken. And as you know, proximity means shallow DOF.
So that is how I can take a picture like this one yesterday with my new iPad (and as sensors go, they don’t come much smaller):
Look at the top left corner: is that blurry, or what?
So when we say that a small sensor does not allow shallow DOF, we mean “from the same vantage point”. That much is true. But if you can get close, you can still get very shallow DOF.