It really does comes down to the ability to adapt the process depending on the team, the company, the project and even the iteration. I see being able to adapt as (partly) a function of transparency (i.e. informational openness), and empowerment.

It’s interesting to map the way companies view ‘agility’ w.r.t. the dreyfus model — quite often many seem to get stuck at the first step, i.e. “rigid adherence to taught rules or plans and no exercise of discretionary judgment”, which is perhaps where thinking along the lines of “We use tool / technique X, therefore we’re agile” comes from.