Wrong.
In the earliest days of radio, stations were put on the air by radio set makers, insurance companies, newspapers, car dealers, chiropractic schools, agricultural supply dealers, department stores, colleges and the like. They were promotions for that business or entity that built them, and it took a number of years for them to "discover" that they could also sell ads, like a newspaper does, to other businesses.
Then, suddenly, the newspapers that did not have stations decided that they saw in radio an ad revenue competitor. Some bought stations and tried to keep the revenue in-house or to restrict revenue going to other stations.
When my stepfather's family's newspaper sold their radio station in the later 1950's, he thought that since "radio is dead, we don't have to have a station to protect our revenue". He discouraged me from going into the business because "TV had killed it". Right.
So "competition" is a relative term. In my case, the Cleveland Plain Dealer saw radio as a definite threat and competitor, so from radio's perspective, newspapers and magazines were definite competition. Papers would be radio's biggest local competitor for four decades. And then TV would take take that role.
Radio had competition since amplitude modulation was used for public broadcasts. In fact, radio was a newcomer to the fight for ad budgets. Read issues of
Advertising & Selling at
www.worldradiohistory.com and you will see how it took more than half a decade for the ad community to even take it into account.