Re 30 seconds. Listening to a bad song for more than 30 seconds does not make the song any better it just hurts your ears more. That said if people are paying for a service to get their song pro critiqued or pitched then it should be done properly even if the song sucks. I can usually tell after only a few seconds if the song is any good but if I am doing a critique then I listen to the whole song regrdless of how good/bad.
I agree that in the real world not every employee of every company follows the rules...some will take shortcuts and with something as objective as judging songs mistakes occur. However whether one listens to all or part of the song it is inevitable that some slip through the net.
Some of the top chart stuff I would switch off after a few seconds as being awful in every way. I have also heard songs that will never make it that IMO are far superior in every way to the crap that is in the charts.
This business is a rat race and the best does not always get a fair chance. Life is like that. It is up to us songwriters and musicians to do our best and hope we get the breaks.

I do not know much about Taxi but from what I have heard they generally are fair and do a good job. But nothing is perfect.

This girl who felt that her stuff was way better than the songs she had to screen is probably right. On the other hand some songwriters and her fellow screeners might think that their stuff is way better. There are mega stars who I do not rate and minnows who I think deserve a lot more recognition. Taste can be a funny thing.

Bottom line is if you are doing a job then take pride in what you do respect the customer and do your best for them. What goes around comes around. Fame usually lasts and instant. You need all the help you can get both on the way up and the way down.