With regards to different airlines going to the same destination, one should surely know who one is flying with! Although, on second thoughts, that may be an assumption too far I suspect!!
Some folk can't even manage to get to the correct terminal where an airline flies from two at the same airport.
Gatwick North last year, Easyjet fly from both North (Ex GB routes) & South
Couple checking in at north (after having been stood next to a large sign explaining which terminal to check in dependant upon flight number, and no doubt with South Terminal printed on their voucher) were rather shocked to find they were at the wrong terminal and had little time left to get to south to check in correctly!!!!!
As for the reference number some have asked for it, some want to see the voucher, some are happy with the passports only! Depends on the airline, the Airport (handling agent or airline staff) and I suspect the experience/helpfulness of the actual person on check in.