Here are some more likely culprits:
* Something loose near the HVAC system: Braking can cause vibrations throughout the vehicle. A loose part near the HVAC system (perhaps a screw, clip, or even a component of the ductwork) might be vibrating and hitting something else, creating a sound that *sounds* like the blend door.
* Brake system related noise: While unlikely to directly involve the blend door actuator, a brake component itself could be making a noise that's misinterpreted. This is especially true if the noise only occurs during heavy braking.
* Vacuum leak (if vacuum-operated blend door): While less common in newer vehicles, some blend doors are vacuum-operated. Hard braking might slightly alter vacuum pressure in the system, causing a momentary shift in the blend door (though this would likely be a clicking rather than a "closing" noise). A leak in the vacuum system is a possibility.
* Coincidence: Sometimes, sounds seem related when they're not. It's possible the blend door is making a very quiet, intermittent sound that only becomes noticeable when other noises (like those from braking) are absent.
What to do:
1. Reproduce the noise: Try to deliberately reproduce the noise while paying close attention to where it seems to be originating. Is it actually near the dashboard/HVAC area, or is it closer to the brakes?
2. Have a mechanic check it: A mechanic can diagnose the source of the noise far more accurately than anyone trying to troubleshoot remotely. They can inspect the HVAC system for loose parts and check the brake system for any issues. Mention the timing of the noise relative to braking.
In short, the blend door itself isn't the likely culprit. The coincidence of the noise and braking needs further investigation to identify the true source.