The consequences of inbreeding are the biggest issue I have with this type of relationship.
Humans have a pretty intrinsic yuck factor to incest. At least, the vast majority of humans do. But the incest taboo seems to attach early in childhood. It's known as the Westermark effect, and basically except for a few rare outliers, it's very difficult for individuals housed together for the first few years of either of their lives to become romantically/sexually involved with each other. This applies whether they're related or not--it's been studied extensively in relation to the Israeli kibbutz system, in which unrelated children are raised communally and refuse to date each other later in life, even with strong social pressure from the adults to do so. On the other hand, siblings raised apart--most often due to adoption--do not feel this visceral avoidance, even when they're aware that they're siblings. Most don't go on to actually have children with each other, but there's a lack of unconscious "yuck".
I think it's overkill to send one of them to jail for this, and I really don't like the double standard that only the brother is facing jail time, and the sister is not. However, I agree that the clip is vague. If they're suing for the right to get married, to file taxes jointly, etc, I'm much less sympathetic to them.
Though I know it's popular in minority circles (and we gays are a minority) to feel we shouldn't exclude anyone or judge others for their actions...full siblings having children together is a very bad idea. Almost everyone is carrying a handful of rare recessive mutations that would have a disastrous effect if someone had two copies of a single one of them, but which are perfectly safe if you've got a normal version of one of them from your other parent. A pair of full siblings have a 25% chance per child of that child suffering from any one of these mutations they both got from the same parent, and for each mutation that either parent has, there's a 25% chance that a pair of their children would both have that mutation. This is order of magnitude higher than the risk in the general population. Many of these mutations will result in massive disability, or childhood death. Despite their massive harm, they aren't purged out of the population because they only have an effect when someone has two copies of the same one, and when the harmful versions are rare enough, they can't be removed from the population faster than new mutations to them arise. Because of the many problems associated with such severe disabilities, it is in the interests of society as a whole that full siblings not have children with each other. This isn't based on vague untested thoughts about needing role models in the home like the arguments against gays or lesbians raising children, but on empirical genetics. I would support the government not extending marriage rights to this couple, if that's what they're after.