The distrust of statistics is not justified. The person who is handling statistics may be a liar or a dishonest person, but that would be the fault of the person and not of statistics.
For example, if a ayurvedic doctor prescribes allopathic medicine to a patient and the medicine proves to be fatal, then in such an instance the medicine cannot be blamed. The fault lies with the doctor. Same is the case with statistics.
The person using statistics should not take them at their face value. He should check the results. Also, only experts should handle the statistics, otherwise they may be misused.
Many economists have most rightly observed, "Statistical methods are the most dangerous tools in the hands of an inexpert. The science of statistics is a most useful servant but only of great value to those who understand its proper use."
So, it can be concluded that if statistical facts are misused by some people then it would be wrong to blame statistics. It is the people who are to be blamed.