These references probably come from the way the individual Roman diplomats would act while interacting with other powers. Part of the Roman belief system was that while acting as diplomats, a person had to act as the embodiment of the Roman state. As a result, they were often came across as haughty and arrogant because the belief in the supremacy of Rome was also a part of Roman culture, and did not show the respect to foreign kings that they were probably used to. Whether or not this actually made them bad diplomats is debatable, because even though this tactic probably didn't engender positive feelings towards the Romans most of the time, it was definitely intimidating which is also valuable in diplomacy.

I would point to the way that the Romans dealt with tribal groups (in particular the Germanic peoples) as evidence that they were actually very good diplomats. They took a divide-and-conquer approach in these situations in order to stop them from coming together to become potentially strong enough to defeat them. They did this by allying with certain tribes, and ostracizing others with a complex system of privileges that they would give to certain groups for their continued cooperation. For example, one tribe might have the right to travel and trade inside Roman territory, but if they started conducting raids, the Romans might take that right away, and give it to that tribe's rival. The Romans were able to do this in many places like Arabia, the German frontier, the tribes in modern day Scotland, Mauretania, the Danube frontier; basically wherever there wasn't a major power they had to compete with. However, this system didn't last forever, and the several powerful and lasting Germanic confederations were created, despite the Romans best efforts, and were a major part of the downfall of the Western Roman Empire.

For the Germans specifically, the way Marcus Aurelius did this in the Marcomannic War is probably the best example. A confederation of tribes including the Marcomanni, the Quadi, the Iazeges, and the Vandals cooperated to invade Rome from across the Danube. After the Romans drove them out, they launched a counter-offensive, and they were able to create separate peaces with the Quadi and the Iazeges before fighting took place in exchange for better terms than they would later give to the Marcomanni, and the Vandals became lasting Roman allies. However, when the Quadi broke the treaty, the were punished very harshly, and their king was deposed.