Not sure I would agree about that... there are only so many ways you can use a sling. There does seem to be fairly good evidence that at least some slingers could outrange some archers. How good the archers bows were is maybe more important than how good the slingers were but I very much doubt it was direct fire slings shooting further than even relatively weak bow.
The rest of what you said- probably right on. Lead bullets maybe puncture skin frequently but I thought most of the argument for the sling bullets was based on blunt force trauma, hence the talk about AP or not. Where an arrow might hit exposed surface and cause damage, a sling hitting even armor unless quite well made and sturdy beneath would pass on more energy to the person wearing the armour while an arrow being much more surface area loses velocity faster etc and causes less blunt damage.
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