I know the books didn't have this either, but man, I would have loved to seen that scene. So similar, so loyal, so different. They are two sides of the coin.
Looking back that is the one scene I would have wanted to see the most.
... and their meeting pre-dates the murder of Jon Arryn. Ned and Tywin were both part of the siege of King's Landing during Robert's Rebellion. Pycelle opened the gates to let Tywin and his army into the city, and the original sack of KL began. Then Ned rode into the city, made a beeline for the Red Keep and found the King dead and Jamie Lannister on the Iron Throne (physically only).
In the moments and days that ensued, culminating in Robert getting chosen as King and Cersei being chosen as Queen - Ned and Tywin would definitely have met and contributed to the eventual decision to crown Robert.