Did O₄ turn out to explain why liquid oxygen appeared to defy Curie's law? If not, what does?
The observation that oxygen did not seem to strictly follow Curie's law (where $1/\chi$ is linear with temperature)  has been known since Kammerlingh Onnes pointed it out in the 1910's. By the late 1920's, it was known that diluting the liquid with nitrogen preserved Curie's law, suggesting that it took oxygen in close proximity to other oxygen to be the issue. 

Fast forward some 80 years, and the computational tools available to us provide some key insight. As one such paper, Ab Initio Molecular Dynamics Investigation of the Structure and the Noncollinear Magnetism in Liquid Oxygen: Occurrence of O$_{4}$ Molecular Units takes a look at structure and properties of liquid oxygen. Quoting from their conclusion:


  In  conclusion, we  performed ab  initio molecular  dynamics  to  investigate  the  noncollinear magnetism  of  a system with an evolving atomic structure. Application to liquid oxygen provides us with a picture in which the large majority of colliding O$_{2}$ molecules assume structural and magnetic configurations which closely resemble those in the O$_{4}$ molecule. Formation of truly long-living molecular O4 units  also  occurs but involves a considerably smaller fraction of O$_{2}$ molecules.


So, it would seem that O$_{4}$ units, whether long lived 'molecules' or temporary short ranged order is the answer to the deviation from Curie's law in liquid oxygen.

Several comments on these O$_{4}$ units - first, as noted in the paper above, 'long lived' means under a picosecond (which doesn't really seem long-lived to me, but...). Further, the authors above point to The Infrared Spectrum of Bound State Oxygen Dimers in the Gas Phase to explain what they mean by O$_{4}$, which they call a "somewhat rigid (O$_{2}$)$_{2}$ molecule".