I feel this is very much discipline-dependent and what you're actually doing.
For instance, in my job, this is literally what I do all day. If I find a project interesting enough I usually ask the person to share the data with me so I can do the analysis myself and get something out of it (coauthorship in a publication, conference presentation or sometimes I just do it because I've never encountered the problem before and I want to learn about it). But if it's very straightforward/not very interesting (which is like 95% of the other projects) then it's really just pointing people to the right test or method and what they should be looking for before analyzing data.
But Statistics is a very, very vast field so I'm sure whatever people do with it depends on what they are working on. For instance, I find it hard to believe that a statistician or data scientist working for Google or Facebook is concerned with whether this or that data should be analyzed using a t-test or not.