Which is correct, 经验非常丰富or 非常经验丰富？
I think you are correct. In grammar，经验非常丰富 means （拥有）非常丰富(的)经验. We usually use a Noun+Adjective to express [Noun] is [Adjective]. 

The TV host is wrong in fact. We should say 他是一个非常有经验的队员/他是一个经验丰富的队员, but can not say 一个非常经验丰富的队员. Howerver, chinese would understand his informal expression casuse we just take it as an error in speak. May be he wanted to say 非常有经验, and suddenly associated 经验丰富, so...