Why does "拒不" mean "to refuse to do something"? http://adm21.cmu.edu.tw/news_detail.php?sn=1572 :

不聽勸告即請其出場，該科成績以零分計；拒不出場，情節重大者，取消其考試資格，並報請有關機關處理。

http://ssdo.gov.taipei/ct.asp?xItem=6344506&amp;ctNode=46432&amp;mp=124011 :

如拒不參加全民健康保險，是否會受到處罰？

In the above examples, I can see that "拒不" means "to refuse to do something".  

However, if I look at the words individually,
拒 = refuse
不 = not
If one uses "拒不", shouldn't it be a double negative, i.e. refuse not to do something?  If it is just to emphasize the meaning, wouldn't “堅拒” be a better choice?
It seems that there are some teachers in school think the same as you do.

This also shows that there may be still debate in Chinese academia about how to explain this, so there might be not a definite answer.

Also, 拒不 is still not considered a word. But as it is used more and more frequently, it is becoming one.

Another article on CNKI might shed some light on how to understand it, (but I cannot access the full article, only the abstract) which lists some similar phrases:

拒不VV
拒而不V
拒绝不VV  

(a little hard to decipher the symbols in the abstract without the full article) The author seems to be claiming that it is two negative sentences "mixed" together.