Here's the study, despite the fact that the article didn't bother to cite it:

http://www.ncbi.nlm.nih.gov/pubmed/26101624

Seems to me that this study is almost entirely useless for forming the basis of any kind of diet or lifestyle advice because:

It was done over 4 weeks. Almost all controlled diet studies are conducted over short periods of time and are therefore useless as the basis of any long term lifestyle advice (if you want to make any difference to your long-term weight you need to make changes that span years, if not the rest of your life). This is almost inherent in diet studies, because most participants won't accept these kinds of things (skipping breakfast) or even eating a particular diet for long enough periods of time. Imagine as a participant being asked to skip breakfast for 2 years in order to give a decent study length. They're either going to refuse to participate, or have a significant chance of failing to comply with the requirements. This is the reason that so many long-term diet studies are observational (i.e. uncontrolled, just looking at what people do naturally). And observational studies can't be used to determine causality (did people who skipped breakfast lose weight, or were lighter people more likely to skip breakfast, for example).

The study is tiny. n=36 is right on the cusp of being so small as to not have any kind of statistical significance. Further, statistical significance is not the same as a significant effect. The effect size in this study is small. The n is small. So how can you use this as the basis for refuting an existing body of evidence? Extraordinary claims require extraordinary evidence. This study does not qualify to invalidate the existing scientific consensus.

They did indeed collect body composition data. Have a look at the following table:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4473164/table/ta...

Now it might just be me, but it looks like what the no-breakfast group lost was fat-free mass. But then I would have thought the mean for fat-free mass and fat mass should add up to the overall mean for body weight, which it doesn't. So either I'm missing something or there's an error in the table.

Finally, check out "researcher degrees of freedom":

http://theness.com/neurologicablog/index.php/publishing-fals...

Overall, a tiny, weak study, with a single slightly statistically significant result being blown out of all proportion. Such is the state of science reporting these days.