Any kind of focus tracking ("AI focus" and the like) requires the camera to refocus between shots, and focusing requires the lens to be fully open.
Also, you can use your DoF test button with aperture set to something small (f/16..) to see how the image looks like when the diaphragm is closed, and you will observe that this is a lot dimmer than what you see in the viewfinder during the burst: the diaphragm is reopened between the shots.
Experiment:
- Set the camera to AV mode with a small aperture
- Look down the lens and press/release the DoF Test button, you will see the diaphragm close and reopen
- Set the camera to burst mode and shoot a burst while looking down the lens: you will see the diaphragm close and reopen
- Repeat experiment for any focus mode (on my 70D, this happens already for "one-shot" AF...)
- At the end of the experiment, erase all the compromising pictures of your nostrils.