As all diplomats across all of time goes, it depended on the situation. I can find no definitive source which specifically says Roman diplomats were known to be aggressive or hostile, but obviously instances of such exist. Instances of the contrary exist also. I’ll elaborate to the best of my ability.

In the Early Republic, we have reports of ambassadors who were stern but fair. Gaius Fabricius Luscinus was a famous diplomat who successfully maintained peace with various southern Italian states, and impressed Pyrrhus by refusing a bribe. In response Pyrrhus capitulated a few concessions such as releasing men for free. (Source: Ab Urbe Condita Libri).

In the late republic, the Helvian Celt Gaius Valerius Troucillus was a part of the retinue of Julius Caesar during the Gallic wars. He was an ethnic Celt and knew the language and land of the Gauls well, he was the personal interpreter for Caesar and was well respected enough to have citizenship. He also served as an emissary to various Gallic leaders.

The Helvians, who were Roman Allies, were certainly no great friend of the Gauls, but the fact that Caesar chose him specifically as a personal diplomat as sorts shows that he was aware that a helvian celt would certainly be more well received by various Gauls and other Celts. He wasn’t simply an interpreter for a Roman diplomat, he was the diplomat.

I bring him up because it demonstrates that Romans simply played to their situation. Were Caesar’s intentions to be rude to Ariovistus (the king that Troucillus acted as an emissary to), he would have sent a a rude diplomat. His intentions here were obviously to find some sort of common ground and agreement, so he sent a Celtic native to him instead. (Much of Troucillus I got from Romanization by Ramsay MacMullen).

These two respectable figures were often invoked and thought fondly of, suggesting that respectable and accommodating diplomats were to be looked up to.

The following is by no means definitive, but I don’t think it is unfounded:

You may find that as the Empire grew to be the masters of the Mediterranean, there will be more instances of dramatic diplomatic instances, such as when Caracalla sent an army along with diplomats to a supposed wedding with the Parthian Shahanashah’s daughter and massacred everybody there. As they grew more powerful, they needed less careful diplomacy and could resort to a sort of big-stick diplomacy where the ambassadors didn’t flatter the hosts because they didn’t need to, and they acted rude and played foul tricks because they had the army and wealth to back them up. You see less examples like this from the migration period, when it became less beneficial to be crass and it became more beneficial to try to assimilate and coexist with various Germanic feoderati. Most instances of rude ambassadors were from Pax Romana

End of quasi-conjecture

In conclusion, a rude ambassador is sent on purpose. An ambassador may act rude because they know that they can, and you may find that when the Romans were powerful they were more often rude because they could afford to be. When they need to act respectful and negotiable, they do. It benefits nobody for Roman ambassadors to be famously rude, and if an ambassador was rude against the wishes of his liege he would surely be punished. I haven’t been able to find anything suggesting that the Romans were more one Than the other, and there are various reports and tales from ancient history of venerable and respectable Diplomatic figures more so than rude or aggressive ones.

Edit: going into the Byzantine era you definitely find many instances of pompous emissaries resorting to grandiose and petty methods of degradation in an attempt to increase the prestige of the Empire and the Emperor, however that’s outside the scope of the question.