SCA Medieval style fighting's #1 priority is safety. The statement I heard that is very true is "It is about having fun and it is not fun when someone gets hurt." I have a very high regard for SCA fighting because of this.

I personally did not join the SCA for the fighting but I did decide to get involved in it. It seems like fun and is good exercise and since it is pretty safe you don't have to worry a lot about being too good. It can be a lot of work just to get in shape enough to get good enough to get the minimum authorization to fight, weapon and shield.

If you are interested in authentic Medieval or other ancient period fighting I have to agree with this guy's webpage:
http://www.users.bigpond.com/roetroc/FAQ.html
that SCA fighting is not what you are looking for. It is also not perfect when it comes to the way the rules are set up like this guy talks about in regards to how armour and weapons are treated:
The Problem of Armour in Medieval Combat Reconstruction - http://ejmas.com/jwma/jwmaart_mele_1299.htm
SCA fighting does make sacrifices in authenticity for safety. There are also politics involved in SCA fighting as to why certain things are done. I can tell you that it doesn't have to be totally authentic to still be a fun activity. The bottom line is that as long as SCA fighters know the difference between what is historical and what is SCA fighting I don't see how anyone in the Living History groups really have anything to deride the SCA about.