I'm afraid your wrong Robert. Dentists can, and do give general anaesthesia, as long as they have undergone the specialist training required, are registered, have the "correct" facility and have the appropriate assistant(s).
In fact the number of general anaesthetics given in dental practice has been steadily rising since 1998 when the first audit was undertaken and guidelines were issued. Although the guidelines stipulate that alternative methods of sedation should be sought, general anaesthesia is recommended for certain groups of patients.