The reason you are asked to quote the reference number is for identification. The airport I work at has flights perated by bmi and flybe and you would be amazed how many people do not know the difference.
There are some routes that both airlines fly and there have been a number of occassions when passengers with the same name were booked to same destination and have gone to the wrong airline counter, therefore the only sure way is to ask for the booking reference to ensure the correct passenger travels with the airline they have paid their money to.
F3G
In the days of paper tickets the information was printed on the coupons in the same format no matter where the ticket was issued, you coild glance at the coupon and within seconds have the information needed to begin the check-in process. With the introduction of e-tkts every printout is in a different format and it is often easier & quicker to ask the passenger where they are flying to rather than wade through pages of hotel,carhire,weather forecast info etc,etc before you get to the flight details.