Yes, as I said, the law is defined broadly but applied more narrowly. There's always the question of degree, that's assessed by the victim (in deciding to pursue the issue), the prosecutor, the judge, and the jury. The legal principle is de minimis non curat lex ("the law does not concern itself with trifles").

But that's the point of crime surveys - you ask people what crimes they've experienced and count the results.

That's not because courts interpret the law narrowly, it's because crime is under reported, and under prosecuted.

Plenty of people get prosecuted, and convicted, for common assault that only involved verbal threats.