Do you have access to /dev?
drwxr-xr-x 17 root root 32768 Dec 28 16:56 /dev
Did you logout and login again after adding yourself to the group?
crw-rw---- 1 root video 212, 0 Dec 26 19:30 video0
cat: /dev/dvb/adapter0/net0: Permission denied
That's not the same file. Can you do the following as user?