As long as you can question the premise and dig deeper you are not reasoning from first principle.
I don't even think it really applies to language but instead to science and means something very different.
Aren't those the same thing?
It seems the author is referring to core beliefs or premises that the business was found on, as well as relationships in the team. The point is to get to 'truths' everyone agrees upon. Not unlike first principles in physics - you just assume because of the amount of evidence, that say, thermodynamic laws are true, and everyone can agree on that.
Scientific first principles are not necessarily objectively true but they are the best we know of. I.e. as far as we collectively know this is the first principle.
This vs. I believe this and I am going to reason from here. Which is much more likely to be subjective.
That is actually a psychological textbook trick - you are more productive in persuasion when you first manage to make your targets agreeing with you. From there you build upon whatever is on your agenda. The important part when doing so in the article's context is to make yourself look impartial, which in itself has an effect of preventing further group tensions.