I agree that singing can be trained, but without some natural talent, you can't really go far. The most you will be is a well-trained singer with a weedy voice.
I've heard some people's voice that sounded like they have lots of potential, strong vocals, nice tone, just that they lack the techniques and training to polish their voice. these people are definitely blessed with a good voice just that they are not that interested in singing so they don't let their voices reach the full potential.
Then i've heard a lot, most of which can be heard on Superstar singing shows, whose voices are totally pitch correct and technically good, but just don't strike any chord whatsoever. Their voices can be best described as mediocre, and all the training in the world ain't gonna make a mediocre singer into Mariah Carey.
I would really like to have some vocal lessons but I just can't bear to fork out the money for it, so up to now I don't even know what I'm doing is right or not. I think singing is a gift, either u have it or u don't. And if you don't, then you can still sound passably good, or even technically good with lots of training.