Wrong. The watch is given all of the saved networks on your iPhone, including the keys.
I really wish people would search before starting new threads...there's gotta be 4 or 5 wifi threads already.
The watch only has a 2.4GHz radio. It only does 802.11b/g/n, so make sure you aren't using 802.11AC. Make sure your 2.4GHZ and 5GHz each have a unique (different!) SSID. Make sure the 5GHz SSID is NOT on the iPhone, so both are connecting to the 2.4GHz SSID. Someone already mentioned the forget/readd trick to get the watch to pick up the SSID (seem a bit of a bug).
Oh...and one more thing. The security handshake between watch and iPhone is done over bluetooth, so if you go completely out of bluetooth and wifi coverage, you will need to get back into bluetooth range before complete functionality (e.g. phone) is restored.
I wish people like you wouldn't post things as facts that really aren't.
1. Everyone needs to realize that there are a bunch of different routers out there... with slightly different implementations of the standards. What is "true" in one case is not true everywhere. We need to quit YELLING at each other on this forum and start to have a real conversation about what works and what doesn't.
2. You state as a fact that that the 2.4GHz network and 5GHz network must have different SSIDs. This is not true in all cases. For me (and others) , everything works fine with a "normal" setup with my router having one SSID and both 2.4GHz and 5GHz networks operating.
Here is a picture from my router showing my phone (Dereks-iPhoneqz) and my watch (DereksApleWatch) both connected to my router (on one SSID) at different frequencies (5GHz and 2.4GHz respectively)... and everything works fine (I have bluetooth off on my phone right at this moment and I can still launch Apps on my watch and make phone calls and everything.
What we need to do is start cataloging what routers we have. For me, I'm using the newest Verizon Fios router: FiOS-G1100
3. You state some incorrect "facts" about the security handshake that are not true. Even with my phone off... and if I power cycle my Watch it still reconnects to my wifi and can send/receive messages and receive email, etc. (Note: you can't launch 3rd party apps without *some* kind of connection (BT or Wifi) with your phone).
There have been numerous reports of people leaving their phones behind and their watch still connects to their office wifi or to wifi at a friend's house. It's pretty clear that the Watch gains all of the Wifi connection info from your iPhone when you pair them... and then uses that as much as it can.
Anyway. Let's quit yelling at each other this and start to have a discussion. One thing we really need is to catalogue the routers... and what worked or didn't work with each router type...