I think there's a bit more nuance in the rules which, thankfully, allow referees to use a modicum of common sense with handballs like Barkley's.
This is all there is in the rules about 'natural position':
- touches the ball with their hand/arm when it has made their body unnaturally bigger. A player is considered to have made their body unnaturally bigger when the position of their hand/arm is not a consequence of, or justifiable by, the player’s body movement for that specific situation. By having their hand/arm in such a position, the player takes a risk of their hand/arm being hit by the ball and being penalised
There is some leeway there around consequence of the action, but it's not a free pass to dive in. The PL guidelines are more prescriptive, but still include allowances for proximity and shoulder height threshold. So if the ball had struck Barkley's hand above his head, that would be different compared to under his arm at below the shoulder.
You can certainly make a case for a handball under the more prescriptive version of the rules that have been in place in recent years, but I don't think it's cut-and-dried and it's sufficiently open to interpretation to allow a sensible decision to be made.