First of all, I should be clear here and say I didn't read the link. I'm interested in your question from the perspective of looking at domestic violence statistics and statistics in general. I don't think that statistics based on documented cases lie- but that's IF we're talking about statistics that are based ONLY on substantiated cases. There are a great many cases that go unreported on both sides (for women and men.) And there are a great many cases that are dropped or reduced and therefore result in no conviction or conviction of a lesser charge. One could speculate men probably do not report as often as women do. Also, based on my own experience (and that of others I know), one could also say that for every case that is reported by a woman (or a man, for that matter), many, many instances went unreported (by the same woman. Or man.) For example, the law intervened on my behalf three times over the course of 15 years (in regard to my ex-husband), however, that doesn't mean he was only abusive three times. (It was too many times to count.) And, there are many women for whom the law never becomes involved. Either they won't report because they fear the repercussions, or no one else intervenes for them (neighbors, etc.) Statistics don't lie. But sometimes they don't give the entire picture. What we "don't see" may be just as important as what we do see, when it comes down to it. What statistics say may well be completely factual, but it's what we conclude from them that can sometimes be faulty. We have to be very careful in how we interpret them, and by what means we use to justify our conclusions. Speculation, even educated guesses, can sometimes be wrong. Also, one should take into account who is using the statistics (and for what purpose)...if it is in order to maintain or justify a position or stance...if there is an agenda behind it that is highly charged or politically motivated, the statistics may be being used in a way that evokes a similarly emotionally charged response. Sometimes people who then are presented with these statistics fail to adequately use critical thinking skills (or become highly influenced or impressionable) because their emotions become heavily involved. They may miss the forest for the trees, so to speak.
And one must be at least a little bit wary of survey statistics. Surveys do leave room for false conclusions because of the potential for biased information, biased answers, and unclear questions, and subjectivity. Surveys rely on people being honest, rely on everyone understanding the questions, and having questions that are clearly relevant, and the survey being distributed randomly...too many variables left unaccounted for (or even the omission of one important or relevant variable) can skew the validity of the interpretation of, if not the, results. Even self-disclosure surveys have the potential to produce faulty results because they rely on one's perception of the event or question. This is not to say that surveys are completely useless. They are assumed to have a margin of error, however. But even the margin of error can be faulty. What I'm saying is, you have to be careful (once again I'm saying it!) of interpreting the results. Research that's done carefully and objectively has the best chance of being reliable. Surveys are not the most reliable means of research.
Another problem is, people like to use correlations as proof or evidence of something. Many do not seem to understand that correlation is NOT the same thing as causation. Proving a relationship between two variables exists does not mean that there is no chance at all of other variables existing that may be acting upon (or even causing) the "relationship." For example, we often see in this forum people who are saying that feminism is destroying the family structure. The people who make this claim are looking at this relationship as if it only had two variables: feminism, and family structure. However, it is likely that there are many other variables that are acting upon this relationship- for example, the economy and society's changing values and norms. So to say that one causes the other, without looking for other variables that may be causing the correlation, is biased and lacking in critical thinking. It leads to false conclusions that may have the potential to be quite harmful.
If feminists are using statistics by the CDC (or any other statistics) they likely are being used as a tool for some kind of agenda. That is not to say that this bad or good. What I would say is that we need to ask ourselves some very important questions: is the tool they are using a reliable tool? Is it valid? Is it objective? Are there things that are not being presented? Are we getting the entire picture or only part of it? How important are the pieces that might be left out? How emotionally charged do we feel after being presented with the information? Are our emotions interfering at all with our ability to use critical thinking? Are we motivated to explore all sides to the issue? Are we forming conclusions or judgments before we have all the relevant facts?
Note: Forgive the long answer, please...I am very passionate about critical thinking and I appreciate the opportunity to explore this topic in relation to your question!