If women were really responsible for 1/3 of domestic violence attacks (the daily mail is too general to know if they are just looking at a survey or accusations) then you would expect 1/3 of domestic homicides to be women on men - this is not the case, so you have to consider what is different and what is being missed. I suspect it is the gradient of "seriousness and context," that is going unrecorded.
What are these reports - does a single hit carry the same weight as a women reporting a decade of continuous abuse? I suspect it does, I very much doubt that every incidence of abuse over ten years would be logged as a separate incident. That is a problem with looking at these figures in a combined way without context.
I suspect that, when accused of domestic violence or a one off attack on their partners during a fight, a lot of men accuse their partners (perhaps legitimately) in return. It is plausible that the kind of domestic violence where a volatile couple escalate things when drunk etc is equivalent between partners - with the man being stronger and the woman coming off worse from equivalent behaviour. My best friend works in A&E and when women present with such injuries, downplaying the fight, it is not uncommon for the same bloke (not a mark on him) to be yelling about how she slapped him and he'll have her done for assault, never see her kids again etc. It would be interesting to see if these reports, from the husband and wife, would look similar on paper - although neither can be proud of their behaviour we shouldn't group this in with sustained patterns of abuse.
The more terrifying and dangerous type of domestic abuse, where a woman is isolated by her children and financial situation and essentially powerless (due to the structures and social conditioning of our current society), is the one that leads to serious injury and murder. We know this differs dramatically between the sexes, as the murder rates are objective, not subjective.
The former, fight type assaults are probably over represented as people feel empowered to report. The latter are underrepresented as it takes so much strength to even get away. More women in the first group is skewing these results.