Well, there seems to be some fairly good evidence that it was Richard, but I don't consider the DNA as hugely important. It shows a possibility that it was Richard III, but I realize that in addition to Richard the man had a lot of other relatives from that time. In fact at that ancestral distance the body could have been almost any body in England and still be related to him.
This is not correct. The DNA they used to determine his ancestry was mitochondrial DNA (mtDNA). mtDNA is passed exclusively mother->child (i.e. fathers do not pass theirs onto their children) and does not undergo recombination (so it doesn't get mixed up generation-to-generation). As such, the extent to which is spreads throughout a population is much less than the extent genomic DNA spreads.
Is it bullet-proof? Of course not. But given the comparator sample was from an individual known to be descended from the king via a maternal line, given the age/location of the skeleton, and given the skeleton had physical traits consistent with the king and his known cause of death, its a pretty strong piece of evidence. The only other possibility would be a cousin/brother, with the same skeletal deformities, who died in a battle at about the same time.
Bryan