Earlier quoted context omitted.
How do you have integrity when you throw your own engineers under the bus?
Integrity is about telling the truth (as you see it), not about doing stuff for the benefit of "your own". In fact the latter can lead to exactly the opposite of integrity.
Integrity means the opposite of being two-faced.
In this case, OP's behavior lacked integrity, even though it was likely honest. Although he was at the Yang meeting as a representative of LinkExchange, he advocated in favor of Viaweb. The forcefulness with which he argued ("your guys are wrong") definitely crossed the line into advocacy, not just an off-hand honest opinion. This set up a conflict within himself (his feelings toward Viaweb vs. his own interests and duties to his partners) as well as a conflict within the LinkExchange team.
https://insighttimer.com/consciousleadershipgroup/guided-med...
https://www.commonsensemedia.org/character-strengths-and-lif...
"the standards of integrity involves regarding internal consistency as a virtue, and suggests that parties holding within themselves apparently conflicting values should account for the discrepancy or alter their beliefs."