I agree to some extent, but I still like to think integrity is a function of how you behave at all times, not just when it is advantageous.
For example in the situation above - I perceive you as the kind of person who really believes what he writes and wants to help people get up and running. I mean, your essays date back before YC.
So in my mind, advising this group during the acquisition offer, even if there was a chance you would miss out, is showing a true adherence to some kind of ethical/moral code.
I agree with froo. This is definitely not a powerless situation, as you got to advise the startup. If you had less integrity, you could easily come up with plausible arguments why should they accept your funding before getting acquired.