The answer from the C-SPAN host is a bald-faced lie. C-SPAN didn't go to this partisan format until the Republicans gained control of the House in 1994. Prior to that, they had split the telephone numbers by eastern, central and western regions of the country. These days, they often don't even make it Republican, Democrat, other — but Democrat, PRESIDENT BUSH, other. Meaning that they personalize their call-ins for and against the president. This when C-SPAN's main reason for existing is to cover Congress.
More importantly, even though their lines are separated by political party, if you listen carefully, the host seldom identifies a caller's party. The host almost always still uses the city from which a person says they are calling. What that tells me is the partisan segregation of callers is for the purpose of screening, only. By not rigorously ID'ing all callers by their partisan affiliation on the air, there is no way for us in the viewing public to know how truly even-handed C-SPAN is — or is not. Personally, I don't think they are, but are skewed very far to the Left.