To paraphrase a former US president:
That all depends on what your definition of Quick charge is...
EVNow, what are you referring to when you say "Quick Charge"?
Battery capacity absolutely affects quick charging, if you are referring to Tesla's supercharger (90 kW)...end users don't care about C rates...what matters for the end user with Quick Charging is miles/hour of charging. Since higher capacities give higher miles/hour of charge, there's an effect.
I agree, there shouldn't be any problem quick charging the lower capacity battery at the same C rate as the larger pack.
I'd say the lack of supercharger support for the base Model S is for at least 3 reasons:
1) Tesla wants a way to pay for a nationwide network of Superchargers...forcing the upgrade to a 60 or 85 kWh pack is one way to help subsidize it.
2) With the base pack, the superchargers would need to be MUCH closer together (perhaps 75-100 miles instead of 200 or so) for base customers to take advantage of them for long distance travel. That might require (VERY rough ballpark estimate) on the order of four times as many supercharger installations.
3) Base pack customers are likely to be getting the car for short-distance commutes, and therefore a NEMA 14-50 is plenty for overnight charging.
I'm sure there are more reasons.
Edit: EVNow, I completely agree with you on a technical front (same C rate shouldn't matter)...I'm coming from an end user perspective, where the customer associates quick charging with miles per hour of charge.