The Line Between Teamwork and Personal Performance

Not sure if it is because I'm paying more attention to it these days or if it really is just that prevalent - but I seem to be running more and more into stories of slackers, poor processes, and the folks that feel they are shouldering a large portion of responsibility.
In one case, a friend of mine works as an on-air talent for a radio station.  Frequently, he has shown up to his remote broadcast with almost nothing in hand that he needs to complete the remote.  These are things like copy points, prizes to give away, etc.
At this particular station these things are to be provided by the promotions department.
But they rarely are.
When the problem was brought up to the GM of the station, the answer was "It's YOUR job to make those things happen if promotions isn't going to do the job..."
And here's where we get to my question:

Where do you draw the line between teamwork and personal performance?

Do you draw such a line?
Or do you just blindly chug away to benefit the overall good of the team/organization?
One of my mentors states that after working under such conditions for a certain period of time - this all becomes a personal choice as to whether or not you want to continue working for a team or organization that permits this type of behavior.
So basically, suck it up or leave.
I agree to a point.
However, a larger part of me feels that you have to draw the line somewhere or you will end up driving yourself bat-sh*t crazy with stress, among other things.
How would I deal with this?
I can actually tell you exactly how I've dealt with it.  And how I've seen others deal with it.
Here they are.  In 3 Steps.
#1  Stop Paying So Much Attention to Everyone Else
How often have you heard this line? "I'm NOT picking up so and so's slack anymore!" or "I'm sick and tired of having to step in because things are not getting done the way they should be!" and then that very person once again picks up the slack or once again steps in to correct mistakes.
I don't know how many times I've felt nervous about something getting done - only to find myself checking in on someone then find myself knee deep in everything THEY were supposed to do.
Stop it.
Actions speak louder than words.  Just stop checking in on people.  Stop dropping all of your responsibilities to help all the time...and be nice about it.
Since you are not making a ton of noise it takes a little longer to gain traction with actions only, but it is a much more solid, long term approach than shouting at everyone.
Just trust that they'll do their job.  Which means sometimes, you'll have to...
#2  Let things fail
Yep.  Let it fail.  I promise - it'll be the only way to shine attention on the slacker.  It's the only way for everyone to see where the weakness lies.  Whether it be with the slacker or the process itself.
You've heard it before, sometimes you have to take a step back before moving forward.
If you are constantly covering for those not pulling their own weight OR you are constantly using workarounds to get things done and make up for a poor process - you'll never gain ground because you will always be in a state of reactive workflow. 
So let it fail.  Then watch everyone straighten up REAL quick.
#3  Keep everything in writing
All the project communication, everything.  If you sent a message 2 weeks ago requesting material for a deadline - then you need to be able to forward the old message when following up.
"Just making sure you got my message last week...never heard back from you." The date and time on the FWD heading will knock out any argument as to whether or not the message was actually sent.
I was questioned recently regarding some incorrect copy on a "Welcome" message following a signup on a conversion form at our website.  Instead of getting all crazy, I simply fowarded the email I sent BACK IN MAY with the change that was supposed to happen.