I totally hear you on “not sure where my work ends and theirs begins”! I feel like every project and team has a different dynamic, and there are no clear-cut universal boundaries for our job descriptions anymore. (Which I like! But it can be frustrating, too.)
When I say “structure first” I’m talking about content models like the kind described by Rachel, which for me often represent the intersection of the larger content strategy with IA (those fuzzy boundaries again!). I do sketches, wireframes, etc as part of my content model, but more as alternate views of the same model so that we can understand it from a number of different angles.