Free radio is not free
Somebody is paying for it.
When radio stations offer "free" air time as part of a sponsorship deal, it may be free to your race, but it's going to be paid for by someone else.
Radio stations do not sponsor events to promote themselves. They sponsor events to acquire something of value they can sell to their customers - like air time, packet inserts, banners, etc.
So, they'll sell the air time to another company, whose name will be mentioned in the spots promoting your event. They'll sell the right to place inserts in your runner packets to another company.
When you sign a radio sponsor, include a provision that allows your event to approve any sponsors signed by the radio station. You don't want a company that conflicts with your sponsors nor one that may be incompatible with your event (like a beer sponsor for a race produced by a local school district).
"Free" radio spots are not donations. They are part of a business deal.