Larry the cable guy wrote:...There are several reasons you would need a race bib.
1) identification in case of a rule violation.
2) it identifies you as one of the 7 varsity members of your team, or as a competitor in the state championships.
3) the bib system with video is used to determine official order of finish at a number of championship meets.
Really, this isn't a stupid rule. The bib has practical applications and you are asked to wear them at every major invitational.
Also, chips don't work 100% of the time. Mayor's Cup in Boston last week one of the guys on our team's chips didn't read at the finish. Because he was wearing a bib it was easy to positively identify him in the backup timing system.
I'm the biggest proponent of "no stupid pointless rules", in this case there are a lot of good reasons why the OP's teammate should have been DQ'd - in fact I'd even say the runner should have been pulled off the course as soon as a race official noticed he or she didn't have a bib on (or not allowed to start, how does the clerk of the race allow that to happen?).
To the OP...to see why this is really an issue I'd encourage you to volunteer to work with the timing crew at any mid-size road race. See aht problems finishers without bibs cause, you'll change your position.