The largest portion of the Scientology contract released by Wikileaks confirms that the new member accepts that Scientology is a religion and deals with religious matters. Specifically, Scientology teachings are religious rather than medical, an accusation that has plagued Scientology for decades. (If anything they did constituted medical advice, they could be prosecuted for practicing medicine without a license.)
One might think the line should be pretty obvious, but the fact is many religions have had to dance this line, particularly when practitioners do not seek medical assistance for ailments but instead follow spiritual advice. Another point of common contention is the cause of what doctors call mental illness, but a religion might call possession. Other religions might call for an exorcism. Scientology might call for isolation, followed by auditing to help clear the engrams limiting the person's spiritual potential.
The one big difference between these examples is that while pro-exorcism religions generally leave the non-religious to their medical beliefs (as well as sometimes attempting to rule out mental illness before judging a case as possession), Scientology is actively anti-psychiatry. Discrediting the profession is a persistent goal of the Church of Scientology. Doing so pretty much requires making medical statements, and that gets them into trouble very quickly.