Can the heart generate its own rhythm independent to the SAN?
Your textbook and review guide are correct, but the missing details may be a little confusing. Yes, the heart has the property of automaticity, meaning action potentials fire on their own at a certain rate, without input from the nervous system. Yes, the SA node typically controls the overall rhythm of the heart because it overrides the rhythm of the rest of the heart.  However, not all cardiac muscle cells have automaticity. Cells in the SA node, the AV node, and to a certain extent, the conducting system all exhibit a physiologic automaticity, that is, they have ion channels that carry what is called a pacemaker current (or sometimes "funny current"), that slowly depolarizes their membranes after each action potential. When this slow depolarization reaches the threshold voltage, another action potential fires. The SA node drives the rate of the heart because an action potential reaches these other automaticity centers, or latent pacemakers, before they would fire on their own. Normal, non-conducting atrial and ventricular myocytes do not exhibit a pacemaker current (except in certain pathological situations), so do not contract independently. So, while the heart muscle is, as your textbook describes it, "myogenic", normal cardiac myocytes (in an intact organ) are not.

This becomes important in cases where the SA node is unable to generate an action potential, is suppressed (is generating an action potential at a slower rate), or other cells with a pacemaker current have increased their rate of firing. In these cases, you can experience an escape beat (a single action potential from a latent pacemaker propagates through the conducting system to cause a heart beat), or an escape rhythm (a series of escape beats).

These are general textbook level principles. You can refer to the wikipedia entry linked above. They are discussed, perhaps more authoritatively, in Lilly's pathophysiology of heart disease. Chapter 1, under electrophysiology, discusses the general principles of automaticity, pacemakers, and latent pacemakers. Chapter 11, under native and latent pacemakers, alterations in sinus node automaticity, and escape rhythms, goes into more detail about the circumstances in which latent pacemakers drive the heart.