I am very much a fan of starting with the big picture.
I like to start my investigation with documemnts like the organisation's strategy, values and similar.
Guy remnded me that not all projects are related to the big picture. Some might be more mundane like applcaition upgrades, or fixing broken business processes. (I reckon there still should be a link, but it can get a bit academic sometimes, so yes I agree with you Guy.)
Regardless of the context of your project, it really is good practice to start at the highest levels and work your way down. If you know the big picture you can take more educated guesses when you hit the grey zones later.
Have any readers come across develoeprs who have never actually met a user? Who don't understand the business at all, beyond a series of use cases? Next time you are talking to the developers, have a gerneral dicussion about what the users do, and what day to day issues they find challenging, even if it's not specific to your projects and see what they say.
(Of course this is not always the case, but it does occur with an increasing frequency.)