The link that I have found that probably explains it better is this one:
http://www.orestadens-kiropraktorer.dk/firmaordninger
About the issue being 'lidt sort snak'. I can not talk about sportshop user, but in my case, I suffer from a chronical hernation of the cervical disk (C3-C5) what causes a lot of pain (in upper back, neck and shoulder), in some moments much more than others. Long time working in front of a computer does not help much to the issue, and even that I try to keep in shape and do regular exercises to release the pain, in some periods the level of pain is very high. Also radial pain to the arm because of presure in the nerves controling the arm located in the column it is quite normal and can happen for 3 or 4 weeks in a row around 3 to 4 times per year. Regular medical treatment will suppose lots of painkillers, anti-inflamatories and muscular relaxants that will severely affect the liver in the long term, what most of doctors also contraindicate. On a practical basis that will meant that the person suffering these issues will have to seek for sygdagpenge very often because of the unability to work because of the strong pain, dizzyness and high stiffness in the upper cervical muscle area. In my case I was checked up in my GP, a fysioterapeut clinic, Hvidovre Hospital and Rigshospital where they end up making me and MRI scanning.
I believe that the concept to give fradrag for these treatments it is in the same category of the deduction of the costs of any private sundhedforsikring (those in many cases cover the total or partial costs of the treatmenst also, but to a limit per year). From the system point of view, it is a much better economical solution the fact that allow fradag to people to get treatments and continue working in an efficient way than to make the report to sygdagpenge and stop their productivity.
Unfortunatelly there is quite a lot of people that suffer of these kind of injuries that they normally worsen by time.
I hope that this helps to clarifies the 'what and why' of the thread issue.
Cheers,