I'm not sure that's correct. I'm pretty sure you can use the watch on any network that the phone has connected to previously (unless the network takes you to a log on screen, you can't use those). If your cell provider supports it, you can even use it to receive calls.Yes, but the phone and the Watch have to be on the same network.
Following page from Apple might help:
https://support.apple.com/en-us/HT204562
Compatible Wi-Fi for Apple Watch
Your Apple Watch can connect to a Wi-Fi network:
If your iPhone, while connected to your watch with Bluetooth, has connected to the network before.
If the Wi-Fi network is 802.11b/g/n 2.4GHz.
For example, your Apple Watch won't connect to 5GHz Wi-Fi or public networks that require logins, subscriptions, or profiles. When your Apple Watch connects to a compatible Wi-Fi network instead of your iPhone connection, Green cloud icon appears in the Control Center.
I'm not sure that's correct. I'm pretty sure you can use the watch on any network that the phone has connected to previously (unless the network takes you to a log on screen, you can't use those). If your cell provider supports it, you can even use it to receive calls.
I am little confused, I always turn off wifi on my iPhone when there is no wifi around so I assumed it uses Bluetooth with iPhone right? Do I have to leave wifi ON even if there is no wifi around??
As others have said, this is not correct. I've received messages on my Watch when I've stopped in at a McDonald's on a run with my phone left at home. I've joined McD's wifi networks before on my phone so the Watch will rejoin them. (It will even do so when the wifi requires accepting the terms and conditions every time, like McDonald's, and even when I've never been in that particular McDonald's.)Yes, but the phone and the Watch have to be on the same network.
Following page from Apple might help:
https://support.apple.com/en-us/HT204562