It's not that the study methods are bogus, but that they don't actually tell us what the headline says, which, incidentally, is not the title of the study. The actual title of the study is: "Demographic and Socioeconomic Correlates of Disproportionate Beef Consumption among US Adults in an Age of Global Warming"

And from the abstract:

The objective of this study was to identify the demographic, socioeconomic, and behavioral correlates of disproportionate beef consumption in the United States.

So the study actually does do a good job of that, because 24-hr recall is sufficient to tell us the relative rates of high beef consumption in different population segments.

What it's not good at differentiating is determining whether it is fewer individuals consuming beef more frequently or a greater number of individuals consuming beef less frequently.

That is to say, 10% of the population consuming >4oz of beef every day compared to 20% of the population consuming >4oz of beef every 2nd day would appear the same. It still does tell us how much beef is being consumed by the population, however, so the data isn't useless.