Technically, Barzini didn't break the peace. The agreement the Dons made was a limited one: They agreed to end the war, and not interfere with Michael's return to the US, in return for Vito providing protection for drug trafficking in the East. Period. Nothing in that agreement prohibited Barzini from taking advantage of the Corleones' apparent weakness by planting flags in Tessio's territory.

Pete's and Oli are right. The Dons respected each others' territories when they appeared strong enough to defend their territories, or when there was no other provocation or opportunity (like Solozzo's drugs deal, which would have helped all of them make money). Vito's day of reckoning would come to pass when Michael returned and took vengeance because the agreement wasn't binding on him. As Vito said in the novel: "Revenge is a dish best eaten cold."