This is true for almost all cases:
7.1.1.2. Date
An origin server MUST NOT send a Date header field if it does not have a clock capable of providing a reasonable approximation of the current instance in Coordinated Universal Time. An origin server MAY send a Date header field if the response is in the 1xx (Informational) or 5xx (Server Error) class of status codes. An origin server MUST send a Date header field in all other cases.
Note the last sentence of the quote. The Date header field MUST be sent if the origin server is capable of providing a "reasonable approximation" of the date in UTC, but there is nothing stopping a server from misrepresenting itself.