An 'experienced' manager (?) really confused me today and I began to doubt my understanding of delay. Can someone please clarify this?

My understanding is that delay is measured when data travels OUTBOUND and not INBOUND. In other words, if my PC sends data to server, we can meausre delay on the outbound, but once the response comes back from the server, we can't measure the delay. It doesn't make any sense to me if this is incorect.
Bottom line, if you get this in an interview, what's your answer?
******** Is delay measured on INBOUND, OUTBOUND or both? Why? *******