The ATX PSU (labeled CX650F here) converts wall power to a maximum of 12v DC. It's metal case is earthed so short of sticking pointy metal bits though the fan grills it is safe to touch.

The rest of the system only sees the 12v DC or less which remains completely safe to touch. The PSU can not (and will not due to fuses) supply enough current to risk fire (like a 12v car battery).

Having the PSU case exposed is electrically identical to having a pc case exposed. Having it opened on the other hand is a danger. PSU capacitors are known to be large enough to kill.