I know a lot of people like that.
I'm from a culture which is perceived as abrasive, harsh, critical, and aggressive in the US. That goes up, down, and sideways. We're often perceived as bullies until we learn to code-switch.
African Americans get a pass here, since most people are familiar enough with African American culture and mannerisms to know how (or at least that) people use language differently, body language differently, and raised tones mean different things. Immigrants don't get that pass. I'm from a culture most Americans wouldn't recognize as a distinct culture -- there just aren't enough of us here.
For my culture, what you described would be a fine litmus test -- if someone is harsh downwards, they're a bully. If someone is harsh up and down, it's a cultural difference. There are other cultures which are more hierarchical there, though.
One of the key things to remember is that people condition to cultural communication styles growing up. When someone yells at me in contexts where an American would totally feel bad and bullied, I don't feel that way. The emotional meaning of expressions and communication styles changes. The same tone-of-voice can convey loss-of-control in one culture, aggression in another, and excitement in a third.
Coincidentally, without cross-cultural background, we perceive Americans as insincere, plasticity, dishonest, and political. Everyone smiles all the time, even if they hate you, and even the most common question, "How are you?" results in a lie.
I'm firmly convinced that the way to inclusiveness is on the receiving end -- it's a lot easier to learn to interpret that an American isn't being dishonest with fake smiles and constant white lies designed than it is to change how one speaks. Receiving end also doesn't mean adopting one cultural style over another.