Urine specific gravity, not that great at estimating osmolality

I have a clinic patient with SIDAH and until the FDA regains some sanity and Otsuka provides a more rational price this will continue to be a frustrating battle. This patient had some pretty typical labs for a patient with SIADH, except for the specific gravity. I don't remember seeing such a discrepancy between the Sp Grav and osmolality before.

I thought a Specific Gravity of 1.010 was essentially isosmotic. But check out this urine Spec Grav 1.012 osm 587. pic.twitter.com/abFhujkdbK
— Joel Topf (@kidney_boy) September 4, 2014

One of the sharpest nephrologists on twitter, Christos Argyropoulos, replied with this reference:

@kidney_boy I got over this myth 4 years ago http://t.co/CBk1EKNYqS
— ChristosArgyropoulos (@ChristosArgyrop) September 4, 2014

The conclusions from the abstract:

RESULTS: This study demonstrated that USG obtained by both reagent strip and refractometry had a correlation of approximately 0.75 with urine osmolality. The variables affecting the correlation included pH, ketones, bilirubin, urobilinogen, glucose, and protein for the reagent strip and ketones, bilirubin, and hemoglobin for the refractometry method. At a pH of 7 and with an USG of 1.010 predicted osmolality is approximately 300  mosm/kg/H(2)O for either method. For an increase in SG of 0.010, predicted osmolality increases by 182  mosm/kg/H(2) O for the reagent strip and 203  mosm/kg/H(2)O for refractometry. Pathological urines had significantly poorer correlation between USG and osmolality than "clean" urines.

Here is a table I made from the conclusions: