Aerobatic engines have scavenger pumps in the sump which then take it to a tank which means when you play silly sods a supply of oil is maintained to the bits that need it.
Okay, I get your point. I don't think you're entirely correct, but I'm not sure. But I think it all comes down to "what's an aerobatic aircraft".
I personally fly the Robin R2160 (and, coincidentally, so does Mark1234). As far as I know the engine is completely identical to what's mounted on, say, a DR400-160 with the one exception and that is that there's a cup or something to prevent the oil from leaking out through the breather pipe when inverted. (Still, anything over 5 quarts is chucked out anyway.) Even the dipstick is in the same place, so I assume this engine has a wet sump too.
When pulling positive Gs (the airframe is certified to 6 G) there are no limitations whatsoever. As far as the manufacturer is concerned you can pull that all day. So I assume the oil pump is fully capable of supplying the engine with sufficient oil even in relatively high-g manoeuvers.
The catch with this engine is of course the negative Gs. The wet sump means that the oil pump will run dry, no longer supplying oil to the engine. Because of this all inverted manoeuvres are limited to 20 seconds or less - we use 10 seconds for additional safety margin.
So what triggered my post was your suggestion that during positive G manoeuvres (loop, barrel roll) in a PA-38 you would shag the engine because the oil pump would not cope. I think this is incorrect. But you would definitely shag the engine in a relatively short time with negative G manoeuvers.