I too have mature oaks (and redwoods), which means lots of jays. I see the opposite, though... hummers chasing the jays. It always cracks me up. Just yesterday I watched a jay trying to get the ripe cherry plums, which are in a [nesting, I believe] female Anna's territory. She should not care about cherry plums, but she chased the jay. TWICE. And the jay fled.
Maybe the west coast hummingbirds are tougher. Or our scrub jays are wimpier?