Nicky's information is interesting and brings a lot of possibilities. This shows that with a bit of familiarity, jumping from the stairs isn't a problem. Cooper's 'trouble with the stairs' well could be a red herring. The pressure bump wouldn't necessarily need for the stairs to slam shut, they would just need to significantly impede the airflow for a moment. This might be done by raising and lowering them quickly, as NB pointed out. And I believe at least one report does have the panel light flashing at the bump. As he also pointed out, once the crew believed Cooper had gone, they might be less attentive to subsequent 'bumps'. Flight is a fluid environment, there are a lot of fluctuations, bumps, turbulences. It's also possible that Cooper wouldn't need to be at the bottom of the stairs to jump, perhaps he could have exited from partway down. It's not KNOWN exactly what Cooper did, so any speculation is valid. 'Believing' or 'doubting' something doesn't make it fact.
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(Apparently not.)