Why does some doctors consider a free t3/rt3 ratio valid and others don't?

Valid for what?: If you are chronically ill, the ratio of t3 (liothyronine)/rt3 (liothyronine) decreases. In patients with kidney failure, other chronic diseases this is called "euthyroid sick syndrome". Emphasis "euthyroid", i.e. Normal. Even if t3 (liothyronine) is low, you don't treat this with thyroid, you treat the underlying condition. I rarely measure rt3 (liothyronine) because it does not tell me anything that is not evident.

Different: Doctors often have differences of opinion. Such differences have their root in differences in training and areas of interest. The field of medicine evolves so fast that it is difficult to keep up with all the latest research, even in one's own field, much less someone else's. No doctor can know it all.