Yes, this is correct. The server can just say “I don’t support your keep-alive request and will just close the connection when I am finished”.
From RFC 2616, Section 14.10:
HTTP/1.1 defines the “close” connection option for the sender to
signal that the connection will be closed after completion of the
response. For example,Connection: close
in either the request or the response header fields indicates that
the connection SHOULD NOT be considered `persistent’ (section 8.1)
after the current request/response is complete.HTTP/1.1 applications that do not support persistent connections
MUST include the “close” connection option in every message.