"All your internet-bound traffic can be routed to hosted security solutions provided by..."
So what's the difference instead of routing it to your HQ? You're just outsourcing security - you still have traffic routed to a central location. Does outsourcing security works? Yes/No/Maybe - it all depends on your security needs and resources. Just IMHO makes little sense to have branches security outsourced, and HQ in house. You have a "split brain" situation that usually doesn't help - especially if there is little difference between the sensitivity of data sent through the Internet and those exchanged across the dedicated connection.