The regulation is about equal access, not free access. Now, the SIP feed contains combined market data from all of the exchanges to which the National Best Bid / Offer (NBBO) applies, so that a broker-dealer can look at the SIP feed to determine nationally what the best bid across many exchanges is and what the best offer across many exchanges is. The Reg NMS mentioned is that the broker can't give you a price (before fees) that's outside the NBBO. (There's an exception if the investor explicitly opts the order out of Reg NMS requirements and directs that the order be filled on a specific venue. Last I checked there are 70-some equity venues in the US.)
The consolidated feeds are necessarily slower than the direct feeds, due to processing delays, unless the exchanges intentionally slow down their direct feeds. There are several companies that will sell you expensive FPGA or IBM Cell-based cards that will locally create a consolidated feed from all of the direct feeds. These cards aren't cheap, but are necessary for trading latency arbitrage strategies, and are also useful for low-latency market making.
Of course the consolidated feed requires a slight processing delay, so unless they intentionally slow down the direct feed, quotes from NYSE will appear first in the direct feed and very slightly later in the SIP feed. The argument here is about if the delay between SIP and the direct feed is small enough to be permissible.
The "public" being talked about is the paying public. Nothing in the regulation requires a free SIP feed, and I assure you NYSE doesn't provide a free real-time SIP feed. The regulation is to prevent selling an intentionally slow connection to everyone, and giving a faster feed to only their top tier customers.
Disclaimer: I'm not a lawyer.