Isis K doesn’t have much motive to claim an attack they weren’t behind, from what I’ve read. Salafist jihadis are decently competitive and vie for the mantle of being the “premier” group that will bring about an Islamic caliphate. They need to come across that way to potential recruits and funding sources to achieve their aims and getting caught claiming responsibility for an attack they didn’t actually do would undermine that credibility in their circles.

I think Isis did perpetrate this and Putin is trying to keep the focus on Ukraine because the alternative is to potentially bring into focus how it easy it was for a bunch of Jihadis to waltz into Moscow and perpetrate a brutal attack because the Russian security apparatus has its hands completely full with Ukraine at the moment.