yeah i was thinking that too, at first, it didnt look like privet to me either, particularly because its not shiny waxy glossy...and also...well different from the feral one i have seen before...
but now looking it up...i think it is. just an unusual species...not the common wild ones...
this is a pretty well developed older tree, yet there arent any baby
trees around...maybe they are hiding out in the nearby woods or something...but basically just to say its not making tons of sprouts right there...as the other privet i am familiar with did...