FX is also a national feed.
That may or may not be typical of CNN or other news channels, but it typically is so for the local channels whether they are broadcasting a national feed (usually) or not. The satellite feed will be the same as far as the programming, but in general, the local markets will feed their own advertising through the line on cue.
When I watch FX here in Southern California, I frequently see commercials that would only interest people living in this area, such as Car Sales from local dealers.
If you are going to spend money on an ad that you have to pay through the nose for in the first place, you are going to want to target your audience to get the most bang for your buck. If you have a National audience, like during major events, you are going to be paying a stunning premium to put your ad in the National Feed. Superbowl ads are a good example for that. As many times as I've seen the Clinton ads here, they would have had to cough up over 2 billion dollars to pay for such an ad if it was being broadcast nationwide (and I'm not talking at Superbowl ad rates).
I hope I'm getting my point across. Whether or not the feed is “National”, as far as the non-all news channels go, the local broadcaster will broadcast their own advertisements negotiated with the client. I have no doubt there is probably some overlap with agreements that stipulate that the local broadcaster must allow such and such amount of National ad time, but I highly doubt that the Clinton ads I've seen fall into that category. However, there is also the reality that the MSM and media in general would not hesitate to “gift” such prohibitively expensive airtime to Clinton if they can get away with it.