In horticultural parlance, this is considered a “double-flowered form” of western trillium. As noted by Ron B in response to silver_creek’s photograph of this same plant at UBC Botanical Garden in this discussion thread, double-flowered trilliums are indeed uncommon, to the point where no named cultivars were known to exist by the authors of a book on the genus. This cultivar predates that book by at least twenty years, but seems to have slipped into obscurity. With the exception of the photographs and discussion on the UBC BG web site, there are no other mentions of it online. Perhaps it has only ever been in the collections of two institutions: UBC BG and the Washington Park Arboretum, the source of the material here at UBC.
An understanding of double-flowering manifestations is continuing to build. It has long been recognized that double-flowered forms are the result of mutated floral organs, e.g., stamens developing as petals. However, the genetics of these transformations, such as which genes are at least partly responsible, has not been well understood until recent years. I’ll have to track down the paper this media release is based on, but for now, please read Genes for Unusual ‘Flower Within a Flower’ are Identified by UCSD Scientists.