The response to this query from A.ISI.EDU would be:
+---------------------------------------------------+
Header | OPCODE=SQUERY, RESPONSE, AA |
+---------------------------------------------------+
Question | QNAME=USC-ISIC.ARPA., QCLASS=IN, QTYPE=A |
+---------------------------------------------------+
Answer | USC-ISIC.ARPA. 86400 IN CNAME C.ISI.EDU. |
| C.ISI.EDU. 86400 IN A 10.0.0.52 |
+---------------------------------------------------+
Authority | <empty> |
+---------------------------------------------------+
Additional | <empty> |
+---------------------------------------------------+
Note that the AA bit in the header guarantees that the data matching QNAME is authoritative, but does not say anything about whether the data for C.ISI.EDU is authoritative. This complete reply is possible because A.ISI.EDU happens to be authoritative for both the ARPA domain where USC-ISIC.ARPA is found and the ISI.EDU domain where C.ISI.EDU data is found.
If the same query was sent to C.ISI.EDU, its response might be the same as shown above if it had its own address in its cache, but might also be:
+---------------------------------------------------+
Header | OPCODE=SQUERY, RESPONSE, AA |
+---------------------------------------------------+
Question | QNAME=USC-ISIC.ARPA., QCLASS=IN, QTYPE=A |
+---------------------------------------------------+
Answer | USC-ISIC.ARPA. 86400 IN CNAME C.ISI.EDU. |
+---------------------------------------------------+
Authority | ISI.EDU. 172800 IN NS VAXA.ISI.EDU. |
| NS A.ISI.EDU. |
| NS VENERA.ISI.EDU. |
+---------------------------------------------------+
Additional | VAXA.ISI.EDU. 172800 A 10.2.0.27 |
| 172800 A 128.9.0.33 |
| VENERA.ISI.EDU. 172800 A 10.1.0.52 |
| 172800 A 128.9.0.32 |
| A.ISI.EDU. 172800 A 26.3.0.103 |
+---------------------------------------------------+
This reply contains an authoritative reply for the alias USC-ISIC.ARPA, plus a referral to the name servers for ISI.EDU. This sort of reply isn't very likely given that the query is for the host name of the name server being asked, but would be common for other aliases.