Yes, precisely. There's a difference between hand-held and long tracking shots. They are amongst many choices you have when leaving the tripod. What you call the docu-style is once again becoming a rising part of the language of film, due to the rise in popularity of "reality television." Audiences are more accustomed to that kind of photography and this can work to our advantage: it works on an audience subconsciously by anticipating tension, placing us in a real situation and foreshadowing not-so-nice events about to happen. A gliding steadicam shot in this instance wouldn't have dealt the same amount of tension. It would have understated the upcoming events instead of raising their stakes.
I'm a big fan of the Bourne trilogy. In The Bourne Ultimatum for example almost all shots are shoulder camera or simulated shoulder camera to keep the tension high during the whole movie. Even when they're talking in an office. But I think my opening shot is a bit too shaky. Halfway between what I did and steadicam would have been better in my opinion but that's the best I could do by hand holding my DSLR cage.