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.
When you’re an empire that has been at war for most of a century the different conflicts become more or less amalgamated. With that, every small loss is actually compounded with every loss from years past in a way that no other military has to contend with.
The same thing also serves as a benefit, as every military victory can be endlessly propagandised and lionised to your civilian base. Meanwhile, the military is aware of the realities and becomes more and more passive (or indirect, for lack of better words) with its actions to avoid the compounding effect of military losses.