It is shown that magnetic states and field-driven reorientation transitions in synthetic antiferromagnets crucially depend on contributions of higher-order anisotropies. A phenomenological macrospin model is derived to describe the magnetic states of two antiferromagnetically coupled magnetic thin film elements. The calculated phase diagrams show that magnetic states with out-of-plane magnetization, symmetric escaped spin-flop phases, exist in a broad range of the applied magnetic field. Due to the formation of such states and concomitant multidomain patterns, the switching processes in toggle magnetic random access memory devices (MRAM) can radically deviate from predictions within oversimplified models.