Step 1: Examine Statement I.
Although lithium has the most negative standard reduction potential,
\[
E^\circ(\mathrm{Li^+/Li})=-3.04\,\text{V},
\]
this does not make its reaction with water more vigorous.
Hence, Statement I is not the reason.
Step 2: Examine Statements II and III.
Lithium has
\[
\boxed{\text{very small atomic size}}
\]
and
\[
\boxed{\text{very high hydration energy of }\mathrm{Li^+}.}
\]
These factors make lithium less reactive towards water than sodium.
Thus,
Statements II and III are correct.
Step 3: Choose the correct option.
Hence,
\[
\boxed{\text{Statements II and III only are correct}.}
\]
Therefore, the correct option is \(\boxed{(B)}\).