This is based on a class given by one of the rabbis at my yeshiva:
Consider the story of Kamtza and Bar Kamtza, often brought as an example of Sinat Chinam. Arguably, the hatred there wasn't without benefit: The rich man didn't want to be associated with lowly riff-raff such as Bar Kamtza. Associating with such an am ha'aretz would have tarnished his reputation as someone who could host talmidei chachamim without them worrying about becoming tameh from amei ha'aratzot.
What it was, was without cause: It's true that in laws of tumah and taharah, if an am ha'aretz's spit touched you or something, you would be tameh and need to go to the mikveh - but that's not really a sin. We know this from the story of Rabbi Yehoshua ben Chananyah:
The Sages taught a similar baraita: Once there was a certain matter needed by Torah scholars. They wanted to discuss an issue with a certain matron whose company was kept by all the prominent people of Rome. The Torah scholars wanted to address the government on behalf of the Jewish people, and they sought the matron’s advice. They said: Who will go? Rabbi Yehoshua said to them: I shall go. Rabbi Yehoshua and his students went to her. When he arrived with his students at the entrance of her house, he removed his phylacteries at a distance of four cubits from the door, and entered, and locked the door before them. After he emerged, he descended and immersed in a ritual bath, and taught his students. Here too, this was conduct that could arouse suspicion that something improper transpired...Rabbi Yehoshua asked: When I descended and immersed, of what did you suspect me? They said to him, we said: Perhaps a bit of spittle sprayed from her mouth onto the rabbi’s clothes. The Sages decreed that the legal status of a gentile is like that of a zav; their bodily fluids transmit ritual impurity. Rabbi Yehoshua said to them: I swear by the Temple service that it was so. And you, just as you judged favorably, so may God judge you favorably. (Shabbat 127b)
In other words, though RYB"C knew that he may be touched by the non-Jewish woman's spittle, he still 'risked' it because the issue at hand was considered more important than that particular din of tumah.
Likewise, in the case of the sages at the meal, rather than nod along with the rich man, they should have calmed him down explained to him that having Bar Kamtza around wouldn't be the end of the world and would not destroy everyone's status as "chaverim" - those that meticulously follow dinei tumah and taharah - because there are just some things that are more important than having to go the mikveh over a bit of spit. It was without cause because the people in the meal - the sages and the rich man - should have realized that it was most certainly not the end of the world if they associated with an am ha'aretz, rather than completely destroying his honor.
So too in the case of Bnei Yisrael - crying without cause: they certainly had benefit: not endangering themselves by going into the land of giants to wage war upon them. But it was without cause, considering that they had seen the might of Hashem time and again prior to that event - they should not have feared entering Israel, at least not so much that they demanded returning to Egypt.
I hope this makes sense.