He's not saying that sudo is dangerous but that a GUI program running in X11 as root is dangerous. This is because most GUI toolkits aren't hardened against attackes (buffer overflows, badly formed events, etc.) that can all be sent as a non-privileged user/program under X11 to one that's running as root. This means that if someone had an exploit in your browser that let them see X11 events or send them to another window then they could potentially use that to gain root access the moment you went into ANYTHING that ran as root under you X session.