I have some experience of this in the UK at least. Here we have feeds from the likes of the press association as well as the official results coming from the electoral commission. However, networks may have their own people at some or all of the counts. These would be local journalists who are attending the counts and will feed news stories back to the studio during the night. They will also get the results from the returning officer and call them in.

In the UK at least we aren't meant to release the results until the returning officer reads them out so waiting for any of the above while showing a live feed of a result would mean we don't have the result to show on screen immediately. For this reason you would likely also have people in the studio watching the live feeds from counts and entering the numbers which would then be double checked against the official feed later. This can be tricky when the result is drowned out by cheering from a crowd of supporters! ie "Labout party, John Candidate 22 thousand... <WOOOOOO - YEAAAH> ...hundred and 1 votes"

The focus for news orgs is getting these results out accurately before their competitors, no one wants to be slow to announce the results.