Edit: it seems like the NYT missed the mark on this one.
AP reports:
Two eyewitnesses, Anna Ravn and Marie Adrian, told the daily BT that they saw a man walking toward the prime minister and then “pushing her hard on the shoulder so she was shoved aside.” They stressed that she did not fall down.
She definitely has a few agents from the Danish Security and Intelligence Service (PET) around her at all times. They are most often dressed in civilian clothing, but you can see the earpiece, they use to communicate.
You’re right, read an article somewhere that also states she always has guards with her