On further reading, I see where I misunderstood: There's one DMA peripheral, but that peripheral has four channels.
/** DMA - Register Layout Typedef */
typedef struct {
uint8_t RESERVED_0[256];
struct { /* offset: 0x100, array step: 0x10 */
__IO uint32_t SAR; /**< Source Address Register, array offset: 0x100, array step: 0x10 */
__IO uint32_t DAR; /**< Destination Address Register, array offset: 0x104, array step: 0x10 */
union { /* offset: 0x108, array step: 0x10 */
__IO uint32_t DSR_BCR; /**< DMA Status Register / Byte Count Register, array offset: 0x108, array step: 0x10 */
struct { /* offset: 0x108, array step: 0x10 */
uint8_t RESERVED_0[3];
__IO uint8_t DSR; /**< DMA_DSR0 register...DMA_DSR3 register., array offset: 0x10B, array step: 0x10 */
} DMA_DSR_ACCESS8BIT;
};
__IO uint32_t DCR; /**< DMA Control Register, array offset: 0x10C, array step: 0x10 */
} DMA[4];
} DMA_Type;
See the "DMA[4]" near the bottom. I'm glad we cleared that up.