It depends when you say "Most of their top stories are obtained from listening to scanner traffic." If it's breaking news, yes, if it's anything else, no. Although this also varies by region. If it's a densely-populated region in a competitive market and you have lots of stringers, then yes a lot of the breaking news definitely comes from scanners. Some people will also call into the newspaper or TV station to tip the news desk off about a fire in their neighborhood or something else going on. Back in the day, TV stations had a dedicated, easy-to-remember phone number for people to call about those things and it was advertised pretty aggressively. If agencies went encrypted and didn't provide the media with other means to gather breaking news, this method might make a comeback someday.
Here in Des Moines, the newspaper has an office in the police station. Not only does this allow a great working relationship, but quick notice of events even without the scanner (the scanner and antenna there are junk). While Des Moines is not encrypted, perhaps this is also the case for other media outlets.
They used to give out pagers to assignment editors as well that sent out announcements and other urgent notices like large scale incidents, pursuits, confirmed fires, haz-mat activation, etc. They are the same notices that get sent to the chiefs. I'm not sure if they still do this.
In other areas, yes, the agencies would also provide no-TX radios for media use. They aren't provided for free; the media has to rent them from the agency.
Also, some agencies like LAPD have online websites where you can read about ongoing incidents that are entered into the CAD. A lot of stringers out there also utilize that. I lost the URL though, sorry. I can't remember if it was just traffic-related incidents on that page or other things as well, but I think it was traffic-only.
If all else fails and you're SOL, sorry, you'd have to rely on press releases and word of mouth.