In fact the latter can lead to exactly the opposite of integrity.
Dictionary to the rescue: "Integrity: 1. the quality of being honest and having strong moral principles."
https://www.merriam-webster.com/dictionary/integrity
Definition of integrity
1 : firm adherence to a code of especially moral or artistic values : INCORRUPTIBILITY
2 : an unimpaired condition : SOUNDNESS
3 : the quality or state of being complete or undivided : COMPLETENESS
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."
Not just any kind of whole. Somebody "whole, united, and indivisible" devoted to his own interests for example, doesn't have integrity (even if he's open about it and e.g. is equally and wholy bad to everybody).
Let's stick to the dictionary: "1. the quality of being honest and having strong moral principles."
The "whole, united, etc" thing is "integrity" in objects (e.g. as in "structural integrity". Not integrity as the moral quality in people.
>Consciously or unconsciously, he was trying to serve three masters: his current company, Yahoo!, and PG's company. That kind of conflict of interest is inconsistent with integrity.
It's the opposite. That kind of conflict of interest is what you want to test someone's integrity.
Someone more strategic or someone which places tactic over integrity would have stayed silent (and neither lose nor verify their integrity). Someone without integrity would have lied against PG's company to promote their own.
Idk, maybe the twitter OP told their engineering team they were worse than Viaweb every day via automated, department-wide emails.
Sometimes that means doing stuff to benefit "your own." sometimes that means blowing the whistle on something. It really depends on the context.