Ah my apologies, I've discussed desirability for pinning instead effect of dynamic hedging on pinning. Yes, you're correct - delta hedging net long ops, will more likely result in pinning.
The example I gave, its part of an expiry correlation arb, while short vol in say indexes, they are long vol in the index components - so not exactly short premium bias if their net position is considered. In this case you'd might see some effects of pinning in the long vol components [topical on strike and size], but not index (as far as I understand they do not dynamically hedge this side of the arb).
So you can see its difficult to discern the inventory and generally categorize who is net long/short- but as Wayne has outlined retailers and funds are in CC's (sell-side long), but there's put buyers (sell-side short) as well as vol/skew-arb funds (sell-side could be net long) etc.