It seems to me that we could get results a bit like that without anyone being grossly dishonest or incompetent, if (1) men and women are violent about equally often but (2) men tend to be substantially more violent than women when they are violent. And #2 seems a plausible-enough just-so story; even if intentions are exactly equal in each case, men tend to be stronger so will do more damage.

(Why would this lead to such results? Well, e.g., officially reported data will tend to focus on violence serious enough for the police or social services to pay attention, whereas if you survey people and ask "have you ever been violent?" or "has your partner ever been violent?" I would expect them to include more-minor violent acts too.)

... OK, I just looked at the paper and behold, that does in fact appear to be the case, and is a large part of why the author says that there is gender asymmetry in domestic violence. (And no, it isn't "somewhat contradictory" to say that one group of researchers finds X, another finds Y, and that on the whole Y is more accurate. The paper goes into quite a lot of detail about the actual evidence each way. The last sentence, aside from acknowledgements and bibliography, is this: "The severity of physical injury and levels of coercion from all forms of violence in relationships appear to be greater for women than for men.")