Step 1: Understand the task.
Four reactions are given and we must spot the one that is not correct, that is the one that simply will not work as written. Let us judge each one.
Step 2: Check option A.
$(CH_3)_3CONa + CH_3Br$ is a Williamson synthesis where the alkoxide attacks a primary halide ($CH_3Br$). Primary halides work well in SN2, so this correctly gives the ether. Valid.
Step 3: Check option B.
Diethyl ether with excess hot HI is fully cleaved to give $2C_2H_5I + H_2O$. This is standard ether cleavage, so it is correct.
Step 4: Check option C.
For the mixed ether $(CH_3)_3COC_2H_5$ with HI, the bulky tertiary group leaves as the carbocation (SN1), giving $(CH_3)_3CI$ and $C_2H_5OH$. This matches the known behaviour, so it is correct.
Step 5: Check option D.
$C_6H_5Br$ is an aryl halide. The C-Br bond has partial double bond character and aryl halides do not react with alkoxides like $CH_3ONa$ under ordinary conditions, so this reaction does NOT happen.
Step 6: Conclude.
The statement that is not correct is option D, the aryl halide reaction.
\[ \boxed{\text{(D) is not correct}} \]