Living with your parents and facing economic difficulty are going to be correlated. If they're included together in a multivariable regression (which is often what people mean when they say "controlling for") then they're going to have multicollinearity and it's not possible to disambiguate the unique role of one versus the other.
It's plausible that the former variable is "stealing" some of the statistical significance of the latter, leaving the researchers with the impression that the latter is irrelevant.
It is, because another way of phrasing that is "coresidence provides no additional explanatory power beyond economic circumstances."
When that's what your data looks like, proper study design either involves testing that hypothesis, or staying the fuck away from making conclusions that take one of those as significant and one as non-significant.
If you have two independent variables that are highly correlated, and you include both into the model, it's going to be pretty arbitrary which one ends up with statistical significance.
If we're dealing with weak effects and small data, there's very little one can do. That's why epidemiological studies like this kinda suck.
Controlling for confounders is better than not; it's also far short of adequate ("controlling" means "reducing a little," not "eliminating"), and in collinear variables you can easily kill the significance of one by adjusting for the other, if you're not careful (ordinarily we experiment with the order of controlling in a multiple regression, to see if that occurs, as well as testing for interaction effects.)
It's plausible that the former variable is "stealing" some of the statistical significance of the latter, leaving the researchers with the impression that the latter is irrelevant.