Due to contractual agreements with the cablecos, cable only channels are not allowed to have regular OTA schedules. The news channels like FNC and CNN and MSNBC do have clauses that allow a small amount of their air time (3 hours a month I believe it is) to be broadcast OTA via an "affiliate station" but then it has to be a breaking news situation that effects the affiliate stations area. National events like 9/11, major disasters like earthquakes that wipe out LA or SF (not your everyday ground shakers) are not bound by the time limitations in the contracts.
In my own stations case, we took FNC for about an hour after the VA Tech shootings because VT is only 90 miles from us and we have a large VT alum population here. After we got our crews in place we broke away from FNC and went live with our own crews and wound up feeding FNC and the FOX NewsEdge feeds to other stations and some of our stuff wound up on the local cableco's FNC feed as well. So there is some give and take in special cases but as a routine thing, it is HIGHLY frowned upon by both the cablecos and the cable channels.