In the first document:
Q. Can I do web authentication with Local switching?
Yes, you can have an SSID with web−authentication enabled and drop the traffic locally after
web−authentication. Web−authentication with Local switching works fine.
1. WLAN, (wlan you want to local switch), Advanced tab, click the "H-REAP Local Switching" checkbox.
2. Wireless, (click the h-reap modify), H-REAP tab, click "Vlan Support", Vlan Mappings button, then map the wlan to vlan you want to drop traffic onto.
Also, for wan up/local switched wlans authentication still happens on the controller until the h-reap goes into wan down. WLANs default to central switching, you have to define the ones which need to be locally switched as described above.