Kyle Richards says there’s more to her dramatic confrontation with a woman on the street … ’cause Kyle claims she only went after her because she was dragging her dog across the street — something cameras didn’t quite capture.

We caught up with the reality television star outside the Beverly Hilton Hotel Monday night … and, we had to ask her about her intense argument with a dog walker earlier this month.

ICYMI … photogs caught Kyle running up to a woman and getting in her face about the way she was treating her dogs — which set the woman off and nearly led to a full-on fistfight.

Kyle — who was with Teddi Mellencamp at the time — says she went over to tell her to knock it off … and only started recording her when she claims she feared the woman might get physical with her.

As for claims that she tried to hide behind Teddi, Kyle’s calling total BS … claiming she wasn’t putting her close pal in front of her.

We also caught up with Teddi outside the Beverly Hilton … and, she gave us details on fighting her battle with cancer. Watch the vid to hear all about it.