I am not too sure why it is essential to have the reference number, it is useful to have in case of problems.
In all the check-in systems that I have used you are able to pull up a passenger by name, no problem. If there are several passengers with the same name the reference number will speed up the process.
The reference number used to be preferable for the self-service machines, but in these days of APIS details being needed for nearly everywhere, your passport and flight number should be better.
Why the staff are so insistent on the number will either be because they have a system that doesn't work on names, or maybe you are encountering the few whose power-craze is giving the whole check-in community a bad name.