It's actually due to both (for different DM particle masses).
https://physics.aps.org/assets/0ce5ba95-0367-46ce-890b-de3a4...
(which is from https://physics.aps.org/articles/v14/96)
https://physics.aps.org/assets/0ce5ba95-0367-46ce-890b-de3a4...
(which is from https://physics.aps.org/articles/v14/96)
This process was first observed only fairly recently, at the Spallation Neutron Source using neutrinos from stopped pions. IIRC, they realized a service corridor under the target room would be unintentionally suitable for the experiment.