I'm not being sarcastic here, but can someone explain to me why it matters if we heard "go" or "get" before "down the hill"?
"Git down the hill" could indicate a speaker with a more pronounced local accent and a more rural background. In contrast "Go down the hill" is grammatically correct and could indicate a speaker with more formal education.
There are, however, some people with alot of formal education who speak either on occasion or regularly with local accents or use local slang. Likewise, some people with little formal education tend to avoid such usage.
As one poster mentioned, it is hard to say much from such a small sample. At the same time, I would have a different general impression of the background of someone using "Git" verse someone using "Go".