spin doctor = not tell truth to doctor?

No. Spin doctor is originally a political term. A spin doctor is someone who characterizes an event or a remark in a manner which it is hoped will be favorable to the employer. So, for example, if a politician says something which can be considered negative, the politician's press secretay would act as a spin doctor, attempting to make the remark sound positive.

The term derives from the use of spin figuratively. When putting a golf ball (in gold, the short shot to sink the ball in the cup is called a putt), or when playing billiards or pocket billiards, it is possible to make the ball spin in such a way that it will curve toward its intended target. This is known as putting spin on the ball. Used figuratively, putting spin on something means to describe it in a positive manner, in a manner which reflects positively on the source.

The terms spin doctor and putting a positive spin on something are now used in areas outside politics. The context you have provided is insufficient to know what the author means, and whether or not he or she has used the term correctly.

It's also a play on words.

The definition above is correct, but since this also seems to be material that speaks about health care, specifically the confusion about what causes cancer, the word "doctor" takes on another meaning. The medical profession (doctors) is putting a "spin" things that cause cancer. (changing studies, making things sound better or worse than they are, minimizing or maximizing studies to make their point)

The proper context would include this:

New Scientist 17 February 2011 (Magazine issue 2799)

http://www.newscientist.com/article/dn20104-spin-doctors-more-harm-than-good.html