It's definitely a colloquial US thing. We say "let's get coffee/beers/lunch sometime" almost everyday, especially when parting as a "see you later". Whether we actually follow up with those invitations here in San Francisco is a completely other story.
Yeah, but that's "let us get coffee" which is normal. The unusual language being highlighted here is "ask to get coffee" without specifying "together" or "with them". Without that, I parse "get coffee" as an instruction, thus meaning asking them to go and buy some coffee for you.
I agree with you that it's awkward; however, "get coffee" is now a colloquial term, which is why most people probably didn't read it the grammatically correct way.
But yes, depending on how one reads, the title takes on a totally different meaning. I usually have this trouble.
I am an American and I though it as asking someone to go get me some coffee like at work. I thought it was going to be that they might pee in it or something.
"Everything I am afraid might happen if I asked a new acquaintance to meet for coffee."