The title seems a little misleading. The study seems to explore the social impact of explicitly declining to answer questions, which is very different from not volunteering something. If I'm telling someone about my work history, the social implications of leaving out that summer I swept freight docks is different from telling them I'd rather not talk about the summer in question given that they've asked.

In the former case, there's no attention placed on that summer, and people (probably rightly) assume that nothing interesting happened (it may come up in an interview why there's a gap there, but I'll get to what I think the parallel for that is). In the latter case, I'm being relatively uncooperative in the information-gathering process.

The connection to companies seems weak to me. When I go into a restaurant that neglects to post its food hygiene scores, I assume roughly the same as when I walk into a store and the cashier neglects to tell me if he has a criminal history. If I ask, and the restaurant tells me that it declines to answer, that seems more parallel to the question of declining to answer negative personal information. Similarly with the "decline to answer" case among people, I bet people would infer the worst of companies that "actively" declined to answer questions (versus those that neglected to bring it up).

These are interesting questions the researcher is asking, and it's particularly interesting to think about how we craft our identities online, but I think they need to reflect more on the parallels they draw before concluding that dynamics are different.

edit: I'm looking up the paper itself, because it occurs to me that a mainstream news outlet is pretty likely to misreport the study's design, results, discussion, etc... and it'd be unfair not to assume that the article writer (or I the reader) misunderstood something.