Actually, having something that matters to you held back by someone's rejection is exactly the sort of thing I'd expect to make a person angry. In most situations it will lead to the rejectee pushing harder for what they want to do - likely a winning strategy in simpler situations.
I think they get messages like this all the time, which is why they think it is funny. So, satire for this specific example, but suggests an increasing level of annoyance from the Y partners when they actually get these messages.
In a nutshell: Make very agent a bit different in the sense that they all won't make the exact same choices. i.e. Rather than have a human always choose the first source, vary this and have some humans that go for the fifth and others for the sixth, etc. etc. Your random selection would also work I guess. Although how well? I don't know.
Then, have a global pattern of how everything should be working, more or less. When a major deviation is found from the global pattern, adjust. How exactly? Those are implementation details.