I had a similar issue using PE edition joining a server running on LAN (from my PC) - we successfully resolved the issue by reinstalling the app on the PE device that was not connecting - all other devices connected so it was rather unusual.
This is certainly worth looking into and appears as an error or bug from a user's perspective. I agree with Jan van's perspective - if this is infact as intended ?- change the language used please in the notification. This error message could have a different note or is worth noting as design feature not an 'error' in the release-notes so we can as parents be more confident we have installed the server correctly for use on LAN environments when not using Microsoft Live ID. Particularly important for younger users like my sons. There is enough concerns about privacy and safety in the world for things like this notto trigger parents to spend time researching this 'feature'.
I had the same issue - reinstalling the Minecraft app on the devices that could not connect worked.