Common drain JFET output resistance "problem"
Here's a good summary table of small signal FET equations from the Sedra/Smith textbook on microelectronics, where \$ V_{ov} \$ is the overdrive voltage which is equal to \$ V_{GS} - V_{tn} \$.

NOTE: The reason why your assumption is wrong is because \$ r_o \neq \frac{1}{g_m} \$. Also, your model shows a common source, not a common drain.