It does seem as if your co-worker over reacted to the situation.
However, I can understand why she's upset.
1) It's her job to track gifts from clients. This was such a gift; she needs to be informed about it.
2) Her co-workers ignored her perfectly normal question. That's rude.
3) Her supervisor blew her off. I suspect this is because your co-worker treated this as "They are being mean to me!" instead of "My co-workers are preventing me from doing my job."
If I were your co-worker, I'd wait until I was calm and then I'd go to my supervisor again and ask for a meeting. In the meeting, I'd point out the following:
My job is to track gifts from clients. It is clear that I'm not getting notified about all the gifts that come in. Is there a way that all gifts can be sent to me first, so that I can track them and send the appropriate thank yous? If I can't get the gifts first, how can Supervisor and I work together to make sure that I am notified of each and every gift? I'd stress that this is important so that I can do my job properly, not because I want first crack at the gifts.
Then I'd gently bring up the fact that there doesn't seem to be a good method in place to distribute the client gifts. Individual co-workers seem to get them and share them around, while no one in authority knows about. This means that the gifts are not shared equally. It would be appreciated by all the staff if a better method of distributing the client gifts could be put into place.
This puts the emphasis on doing the job correctly, which is really the key point that you want to bring up to the supervisor. It also addresses the problem of who gets the gifts, but without pointing fingers at the co-workers who were fighting over the tickets.
I suspect that the co-workers were ignoring your friend because they didn't want her to get a ticket. If the distribution of the gifts can be put into an official rotation or something, that problem would cease to exist.