Are all the teachers at Hogwarts professors?
Based on all the information available in the seven primary books, the answer seems to be that yes, all teachers at Hogwarts are professors.
Except in instances where teachers refer to each other by their first names, every teacher at Hogwarts is referred to as "Professor" by both students and their fellow teachers. In Half-Blood Prince, Dumbledore corrects Harry when he refers to Severus as "Snape", saying that it's "Professor Snape".
To complete the circular logic: because they teach at Hogwarts. That seems to be the only requirement for being called "Professor". If there are others, they're definitely not explained in the books. That said, there's generally an assumption - Defence Against the Dark Arts aside - that if you're teaching at Hogwarts, you're probably an authority in your field (even if that's not backed up by being good at teaching); "Professor" strikes me as a suitable title to communicate that status.
I also think that talk of what it means or how it's used in the US or the UK just confuses the issue. We're not talking about the US or, even, the UK; we're talking about the Wizarding community. Just because they share a word doesn't mean that it has the exact same meaning or connotations as it does in the Muggle world.