Extracting DNA from fossils is actually a thing now, in certain extraordinarily rare circumstances. However, that's not the case here. The genetic studies that

Extracting DNA from fossils is actually a thing now, in certain extraordinarily rare circumstances. However, that's not the case here. The genetic studies that the news piece mentioned were carried out in present-day hagfish and present-day vertebrates. The scientific contoversy is that some taxonomies based of genetics classified hagfish as a kind of vertebrate, while taxonomies based on other methods might classify them as a seperate branch of the tree which split off before vertebrates. What the new fossil showed is an example of an animal that appears to be a hagfish with some features that are characteristic of vertebrates. This is more in line with the theory that hagfish are a kind of vertebrate.