Pete,
You are right stairwells are a safe area.

In most modern high rises the stairwells (or fire towers) should be equiped with self closing doors, panic hardware, increased lighting, vents and sometimes fans that open either automatically or can be controlled by building engineers/fire department. Yes, opening up a door may let smoke into the stairwell of onto your floor however if the door isn't blocked open the damage should be minimal. Of course a smoke charged stairwell shouldn't be entered and another means of egress should be found. In some cases the FD may choose to use a tower for fire operations and restrict access to that one while the remaining towers are used for escape and rescue. Once you enter a tower you should not exit unless you have reached the outside or are directed by the FD. Of course, it always isn't that simple and some situations may require different actions. However, getting to safety without harming others should be your number one priority.

Today, especially after disasters like One Meridian Plaza, MGM Grand Fire and Pioneer International to name a few, highrises are much safer than they were in the past.

You did the right thing, and reconize your mistakes (not checking the doors is a major one). So... this was practice incase the unthinkable happens.