HD most certainly affects analog signals. The generic name for this type of transmission scheme is IBOC -- for In Band, On Channel.. and the whole point of it is the digital signal can be piggybacked onto an existing station frequency.
That said, a station with this system wouldn't be interfering with itself. As you get farther from the station, the digital signal, which is much less powerful than the analog, gets weaker just as the analog channel does, so the digital modulation is never enough to hurt the station's analog signal.
The same can't be said of another station's digital signal. The digital portion of signal on a neighboring frequency in a neighboring area could curtail WIZF's coverage in that direction. That's probably the number two complaint of critics of HD-Radio. (Number one is probably the very short range in digital mode.)
But people simultaneously reporting problems with Wiz's signal in a couple of different directions could indicate a different type of problem.