Just because you didn't allow it on your local WiFi doesn't mean it did not connect to the Internet. Your neighbors might have a guest WiFi it can use. Or maybe it has a built-in cell modem. Your data is valuable, there's reason to put effort into getting it.
Xfinity (aka Comcast) routers broadcast a separate network for Comcast subscribers do use from their phone. I don't think it's unreasonable to think that Comcast and TV manufacturer's could have an agreement that would allow TVs to connect.
Using internet access doesn't seem to be illegal. If there's no password you can't even argue it was protected. Residential proxies are legal too (as they should be - fuck cloudflare).
That's what the Ask button is for with the summarize option, to not have to watch unnecessarily-long videos. Apparently it does connect to public hotspots, often run by major providers.