Your results are on the low side but in range so his viewpoint makes some sense.
If you're determined to be treated, you might have to go to an anti-aging doc or clinic. They often apply a different standard and will treat "suboptimal" (read subclinical) testosterone levels.
But are you sure your fatigue is due to low T? Fatigue can have many causes. Recognize the huge commitment that TRT represents and that years down the road it may feel very different to have gone into it because you had no choice rather than having done it "electively".
This is not to diminish the positive effects that taking your levels from 350 to 1000 can have, but the rest of your life is a long time. Don't rush into it and spend some time researching the pros and cons.