EDIT: Another interpretation of the statement suggests they take responsibility for the event by proxy of deterring said aircraft which was then targeted by friendly air defences.
EDIT II: Prev. statements by Houthis suggest they had formulated new tactics to tail fighter craft with drones/missiles a while back so probably more likely that had something to do with it.
Ansarollah have historically followed up with evidence of such claims against UAE/Saudi aircraft of the same generation. They definitely have the capability, but no hard evidence yet.
they have said it's friendly fire but not anything along the lines of "they fooled us using a drone to tail our fighter and we blew up our fighter jet"