Hmm, powering down the TV broke the connection, yet maintained it when you actually unplugged the internet cable connection FROM the Router? That's the test that would prove to me it's not routed out of that specific router.
You have multiple routers in your system. More than one is likely active with an internet connection. At least that's my initial suspicion, and it is possible it has established a connection from the TV to the router and possibly made it to another router on the WAN jack or possibly even the Wireless connection point.
I do find it interesting that the TV power down does break the link.
Now, you can try that test...inform me if the TV is using a Lan cable or Wireless connection. Also it would be helpful if you told me your local router is connected via lan or it's wirelessly connected as a repeater/bridged wireless connection.
I would suspect Lan connections if the business requires a more secure connection.
We may want to bring in a Networking expert in on this from Just Answer.
I work on TVs and other electronics, and have some basic knowledge of networking...but I really don't consider my Networking knowledge at the same level as an JA Networking expert.
But it's obvious to me that if you turned off the internet...and found the TV could STILL NAVIGATE your browser connections/pages....it's still maintaining the link to the server it connected to and back to your webpage.
One thing I believe the network experts can do...I think they can connect remotely to a nearby computer in your "TV room" ...you have to establish contact with them, then they send you a permission request key that you allow. From that point...they could possibly pick up the TV's TCP/IP of the TV set on the network, maybe see what the destination address is in the Header of the packets.
From that point....it gets beyond the tools I have. I have electronic repair tools, I do not own electronic computer networking software capable of reading destination headers.
Listen, I might be down for several hours. Maybe 8, up to 12 hours. I don't know myself. It's time to do a serious maintenance update on my computer. Complete wipe of operating system.
It might be a perfect time to talk to the Network experts, see if they can make the TV think it's routing to the internet when it's actually routing to the company's server.