Both of those quotes are from the same guy who thinks that mass x velocity tells the whole tale of projectile effectiveness. The first quote doesn't really address the argument of slings vs bows at all, it merely states that slings were not wholly ineffective. The second quote is more of the same, plus its final unsupported sentence.
Use your GoogleFu. I found this on a wiki:
Ancient peoples used the sling in combat—armies included both specialist slingers and regular soldiers equipped with slings. As a weapon, the sling had several advantages; a sling bullet lobbed in a high trajectory can achieve ranges in excess of 400 metres (1,300 ft).[17] Modern authorities vary widely in their estimates of the effective range of ancient weapons. A bow and arrow could also have been used to produce a long range arcing trajectory, but ancient writers repeatedly stress the sling's advantage of range. The sling was light to carry and cheap to produce; ammunition in the form of stones was readily available and often to be found near the site of battle. The ranges the sling could achieve with molded lead sling-bullets was only topped by the strong composite bow or, centuries later, the heavy English longbow, both at massively greater cost.
Caches of sling ammunition have been found at the sites of Iron Age hill forts of Europe; some 40,000 sling stones were found at Maiden Castle, Dorset. It is proposed that Iron Age hill forts of Europe were designed to maximise the effective defense of slingers.
The hilltop location of the wooden forts would have given the defending slingers the advantage of range over the attackers, and multiple concentric ramparts, each higher than the other, would allow a large number of men to create a hailstorm of stone. Consistent with this, it has been noted that defenses are generally narrow where the natural slope is steep, and wider where the slope is more gradual.
And, although there is some speculation and discussion back and forth, the majority of the pages I've found say things like this:
I go by the rule that, being the model users of efficient weapons of warfare, the Romans wouldn't have used them if they didn't work well. Yet they used slingers all the time to screen the advance of their legions and to harry the advance of the enemy.
I agree again with your hypothesis. Sling bullets should deal crushing damage. There is not enough of a sharp penetrating point to cause penetration of any major type, although their might be some minor PEN damage. Plate would protect but chain, ring or leather less so. More like mace or impact-weapons
Yet, from another site, and common to most of them, is the point that slings don't penetrate against armor as much as they lead to blunt trauma that can be delivered through flexible armors like chain.
From Here.
Based on anecdotal evidence a lead shot can punch an inch deep dent into corrugated iron. Just imagine what that would do any flesh beneath the metal armour. You don’t need to imagine too much as we know from historical documents that the ancient Roman army surgeons had a special set of forceps used to extract shot that was embedded into combatant’s flesh.
So, we have a ranged weapon that matches if not exceeds the longbow in terms of range and damage, and it is also a damned sight easier to make it, as is the ammunition it uses. An effective sling is made from natural fibres such as hair and flax, which is pretty easy to come across almost everywhere. Although it is time consuming to weave a sling, once you know how to it, practice will reduce the time taken to make more. And compared to the time required to make a compound bow or to treat the wood necessary for a warbow, it was really very little time at all.
The popular opinion seems to go against your comment that "slings doing more (damage) vs. chain than arrows is idiotic".