PC PSUs have ground references outputs. That means the 0V line is connected to the chassis ground.
You can't simply connect 0V on one PSU to +12V on the other, because it would be the same as connecting 12V on one PSU to 0V on the same PSU - since both PSUs share the same ground.
While, theoretically, you could disconnect mains ground from one PSU and insulate it so that any metal parts on it do not come in contact with the other PSU, this is a dangerous solution - indeed, it may not even work, as some PSUs don't regulate correctly without a good ground.
It essentially can't be done safely and simply.