In other words, "you scratch my back and I'll scratch yours."
People often times forget that in any relationship there should be give and take. Often times the narcissist in us prevails and we focus only on what we can take from others. This is bad karma!
Being in the customer service business this Latin phrase have proven itself countless times as I deal with both internal and external customers.
Leading a project involves inter-department and vendor coordination. As such, it is important that you have a good working relationship with them, otherwise, support will be a very rare commodity for you---and your project---is doomed from the start!
Striking a smooth working relationship with other people entails a lot of giving and less of the taking. This like saving for a rainy day. The more you give, the more emotional bank load you invest. This way whenever you are on the negotiating table there is always a compromise to all conflicts and the willingness to arrive at a win-win solution.