Many radio "voices" come not only from genetics, but from equipment. Knowing how to truly use a microphone, can have amazing results - and broadcasters and performers alike, who are serious about their craft, will carry their own mic with them at all times instead of simply using "house" gear for a performance.
"I sound different on the phone/radio/video recording" is very true. Proximity, angle, filters, brand/model of mic, not to mention post-input filters and EQs, can completely alter your voice - and that's not counting things like the goofy tone-generation "altering" software. For example, using a Shure Beta 87C, you can get a LOT more low tones if you put a wind filter on it, get super close, and talk quietly. Step back 4" and talk normally? You get a more mid-tone. Move back even further, and belt it out? COMPLETELY different sound. Move off to one side or the other? Massive attenuation, which is great for singers - all they have to do is move to the side to "fade" their voice some, instead of straining their vocal cords to get the same result. Dedicated studio microphones (the 87C is a live performance mic) are similarly "workable" based on their pickup patterns, frequency response, etc etc.
Not a broadcaster per se, but an amazing voice, is David Draiman of Disturbed.
Most folks know Disturbed for:
But...David has an AMAZING voice. Example (safe for the non-metal-heads out there - TRUST me, you need to listen to this):