There are Peshatim about or why Kamtza was at fault. However, the basic Pshat is definitely as the Wolf writes.
There are three stories mentioned together: Because of Kamtza and bar Kamtza Yerushalayim was destroyed; because of a chicken Beitar was destroyed; because of a wagon wall Tur Malka was destroyed. Now, I’m sure you’ll agree that the Gemara is not vilifying the chicken. It is merely pointing out how a city was destroyed through a trivialty.
As for the Sinas Chinam, the Gemara asks, whereas in the first Bayis there were the three cardinal sins, by the second Bayis we know who they are and they were great Tzadikim. Why was the Bayis destroyed? The answer is Sinas Chinam.
I ask, who exactly were the great Tzadikim, the Sadducees? The Baryonim? I don’t think so. In fact, the Gemara wouldn’t have had such a hard time finding a Cheit.