I spent a couple of years playing ATC, and without actually looking in the ATC bible, FAA Order 7110.65, I can tell you that terminal facilities are supposed to get the ATIS on "initial" contact.

Enroute centers are different.

Anyhoo, as a pilot, I just give it both to clearance and ground (sometimes ramp, too). Easy. And even if you do that EVERY SINGLE TIME, many times the controller will give you the ATIS anyway. They have to cover their *ss, so it becomes a reflex action to just always do it.

My ATC reflex action in the tower was to always say, "confirm you have ATIS XXX", even if they just got through saying it.