"Women who are insecure about relationships fantasize about anonymous sex and submission more, according to new research."
Study structure dictates much. I'd have to see what their operational definition of "submission" is. It may not be what we think.
Further, the research design -- how they measure their variables, like "insecurity" -- may be unusual or faulty.
Really, never judge by appearances, or anything with so thin a veneer as "new research". Findings are and should be given weight according to
reliability -- that is, repeated studies coming to the same or similar conclusions.
The truth of matters has a way of being revealed in patterns over time, not by a single instance.
That said, it's entirely possible the findings may be valid. Everyone has a degree of insecurity, and psychological studies are better taken as making generalizations about people than absolutist statements. There may be exceptions -- anomalies, results that fall outside the standard deviation -- but it doesn't make the broader findings invalid.
Go and do the footwork of finding the actual research, read it, and figure out from
that if you agree. Working from a vague, secondhand report with details glossed over and possibly biased to "pop" in a publication like "Cosmo" does no one any good.