Applications run on the MCU connected to the BCM43362.
Wiced SDK supports multiple MCU paired with BCM43362. ThreadX and FreeRTOS are integrated to the Wiced SDK along with NetX, NetX_Duo and LwIP libraries.
BCM43362 is the WiFi radio + SDIO.
Your understanding is correct and you cannot run any code on the BCM43362 nor is the source code of the Wi-Fi firmware available.