Sentence first, verdict after

It isn't crazy to think that maybe information problems have people are consuming a less healthy diet than they'd otherwise eat. If people had an underlying desire to eat healthier foods, you'd expect that providing more information might change their choices. 

But if provision of information didn't change their choices, that tells us something too. I'd interpret it as saying that people had basically been making the choices that were right for them all along and that information problems hadn't been affecting decisions.

Public health people conclude differently:

University of Auckland researchers looked at the way in which shoppers used Traffic Light Labels and Health Star Ratings on various food products and were surprised to find the labels made little difference to which foods were purchased.

The study's lead author, Professor Cliona Ni Mhurchu, said people who were interested in healthier choices used the labels more than the majority of survey participants, but overall none of the labels significantly changed what people bought.

There were other ways people could be encouraged to eat more healthily, including making healthier food available in different settings such as schools, workplaces and hospitals, she said.

"But what we also know is unhealthy food is readily available and heavily marketed so we really also need to be looking at marketing regulations."

Professor Ni Mhurchu said the government needed to become more involved in setting standards around how food was marketed, rather than leaving that to the Advertising Standards Authority.

"[Advertising is] not being monitored, [it's] not being evaluated, it's not the government setting the standard."

If you have really strong priors that nobody would choose to eat potato chips if they had full information, then showing that people don't stop buying potato chips when there's a health star rating on them only shows that people are too dumb to interpret the ratings. In that view, maybe we need plain packaging and big graphic health warnings. 

The same data always has multiple possible interpretations I guess. But the health people never seem to weigh the chances that a lot of people have different preferences and goals than the health people would like them to have, and that those preferences are also worthy of respect.