I don't think that returning a tennis serve is a literal reflex as you're claiming.
From my understanding a reflexive move requires some sort of stimulus, and there's no way that your spine can have stimulus of an incoming tennis ball unless the eyes and therefore the brain are involved.
My post isn't clear, in that case. I'm not claiming it's a literal reflex :)
A top-flight tennis player is responding extremely quickly, and extremely accurately. Deliberate, planned action is not happening. It's something else. It's not a spinal reflex, it's something that involves parts of the brain to very rapidly 'orchestrate' a highly complex musculoskeletal dance.
The raw processing necessary to coordinate that dance cannot (in my understanding) be achieved by familiar neurological pathways -- observing, planning, deciding, coordinating. The planning and deciding aspects are bypassed. Only a tiny fraction of the observing aspect is used, such as the moment the other player strikes the ball (because the ball then moves too fast to react to). Some form of prediction happens. Then a number of 'movement primitives' seem to be selected and orchestrated. Ideally, the whole system is tweaked in real-time based on feedback (visual, proprioceptive) regarding whether the goal was achieved -- i.e. did you return the serve well.
It's wild.
It's also possible I'm mis-remembering and mis-interpreting some of this stuff :)
From my understanding a reflexive move requires some sort of stimulus, and there's no way that your spine can have stimulus of an incoming tennis ball unless the eyes and therefore the brain are involved.