I don't think it's instinctual for TWH or Racking horses. Most people have to work pretty hard to teach it. I wish my 17h monster would park out. A vertically challenged riding buddy of mine has taught hers to do it and it lowers the stirrup a good 6 or 8 inches when he does it. Very handy indeed!
I'll bet the pony was shown in hand and was taught to do it. Her response is probably a mixture of fear and stubborness. Like you've said before, even though you've never hurt her, she still thinks you're gonna kill her anyways. She's always got that concerned look in her eyes.
I wish I could communicate mind-to-mind with her. She's a puzzle.
It would lower the stirrup if you could get yours to do it, but they also aren't real strong in that position, at least the pony looks pretty hollow in the back and easily tipped. ;~D