Riot cannot legally take an idea directly "as is" off the boards. If the idea were vague enough that they could just change the name and abilities somewhat, then they could pass it off like they just had a similar idea. However most concepts on the boards are quite specific, leaving Riot unable to use this method.
For an idea to be used off of the boards as it was intended by it's creator, Riot has to hire that person on as an employee to legally use that idea without legal ramifications. Once the champion was made and placed in game, Riot could then end the employment of the concept owner, and legally keep the champion as a part of league of legends.
However most people do not wish to lose control of their champion ideas to someone else. This is one of the things Riot must face when it comes to champion concepts, and is one of the things that prevent them from reaching out and asking to use the concepts. Due to people claiming ownership of their concepts, Riot runs the risk of being sued should they not keep exactly to the creator's specifications for the champion. Even though there are ways around this, Riot does not want such incidents to happen and wishes to avoid these confrontations.
I can't give you all the reasons Riot cannot accept champion concepts, as I do not know them all. I only know a few reasons that I gave some serious thought towards. This is one of the reasons I stopped pestering Riot about accepting champion concepts.