I think your system admin is slightly confused about what exactly a port and a file descriptor are.
Each server has 65536 ports numbered
65535. A program can listen on a port for requests from clients and process them accordingly. Only one program can listen on a port at any given time. In this regard, ports are a limited resource - though it's extremely rare to use most of those ports.
When a client connects to the server, a file descriptor is created for the connection that represents the socket. You can read and write to this socket like any other ordinary file. The number of file descriptors available is huge but there is usually a limit on the number of file descriptors that one particular application can use.
Also, it should be noted that Apache can be configured to listen on more than one port simultaneously.