Er…
Not wanting to speak for Michael, but I think the question isn't whether or not Bisping trained with "Yawara Ryu", it's the idea that it's a "traditional form of jujutsu"… it ain't. The name alone gives away that it's got little to do with anything traditionally Japanese (despite the idea of them teaching the "traditional Yawara Ryu techniques" etc)… in essence, it's a modern, Western eclectic system based dominantly in early Judo (although the connection is, well, not so easy to determine… lots of name dropping, but that's it… no actual connection to the group, especially considering the decades between the people named dying and the founder being born…), a whole lot of other methods (Ryukyu Kobudo) with no mention of where the methods come from, a Ryu-ha, a lineage, or anything tangible, as well as the ludicrous photo of "sword training", showing the most amateurish "demo" technique that no credible system even considers, and the usage of a Tenshinsho Den Katori Shinto Ryu video to show "sword techniques" on their webpage, something to which they have no right to claim association.