Maybe a simpler way of explaining this. I have a similar setup, with an Onkyo AV receiver / 3D system
The TV is connected to the internet via a port on my Modem / Router ( isp supplied Netgear) The smart TV's don't need to sit on your network, so just require a free port on your modem if you have one.
The Onkyo is connected to the TV, and I have a 32" smart TV in the bedroom which is also hardwired to the Modem / Router.
My AE acts as a bridge, boosting the 5GHZ signal for my IOS and Mac laptops. I have tried connecting the smart TV's to my network via my Time Capsule, which also works if you have free ports.
Basically, the TV's just need an Internet connection to access their "Smart" functions. It varies by make, but out of curiosity after reading this, I tried connecting the newer of the 2 TV's...The Toshiba 32" in the bedroom via the Ethernet port on my Airport Express. It found the connection fine, but the Sony in the lounge won't...It needs a direct connection via the router.