I was able to use my Watch downstairs all day yesterday while my phone was upstairs on my bed, and I live in a fairly large home and was definitely outside of wifi. However, later in the day when both were right next to each other I turned the bluetooth on my phone off and wasn't able to use Siri on my Watch.
I remain puzzled. Immensely.
I did some test about this issue. And my found is that the watch's Wi-Fi connection is not as strong as the iPhone. The Watch need to be much closer to the station (or remain line of sight) than the iPhone to have Wi-Fi connection.
Since there is no indication about the watch's Wi-Fi status, it's really hard to realise that the watch is out of range (you need to check the client list on the access point).
I tested it with my normal network setting (one TC at the upper floor, and one TC at the lower floor), the watch is not working quite well (lost connection at certain location). And then I install an extra airport express as a Wi-Fi extender, it makes my watch able to perform all over my place now.