How is enthalpy change equal to heat supplied at constant volume?
No the book is not completely wrong.If you read the next 6 lines then you will find that it wants to point that this approximately true only for solids and liquids, not for gases.

From the First Law,

$$\Delta U = q + w$$
and since work done is $0$ in an isochoric process (constant $V$),

$$\Delta U = q_V$$

Furthermore,

$$\begin{align}
\Delta H &amp;= \Delta U + \Delta (pV) \\
&amp;= q_V + \Delta (pV)
\end{align}$$

Since we are considering solids and liquids, the changes in the volume of these matter upon changing pressure are negligible (as they are incompressible matter) when compared to gases, so the $\Delta (pV)$ term can be considered negligible.

Therefore

$$\boxed{\Delta H \approx \Delta U = q_V}$$

for these incompressible solids and liquids. However this fails when we consider gases as the term $\Delta (pV)$ will no longer be negligible. 

Comparison between the $\Delta (pV)$ values for different states of matter, being heated from $20\ ^\circ\mathrm{C}$ to $30\ ^\circ\mathrm{C}$:

$$\begin{array}{c|c}
\text{Substance} &amp; \Delta (pV)\text{ / J} \\
\hline
\text{Air} &amp; 2850 \\
\text{Water} &amp; 0.1 \\
\text{Iron} &amp; 0.0004
\end{array}$$