I don't think they're breaking into their system at all. They're just abusing a public interface on their sight. A more apt analogy would be repeatedly calling their phone, or ringing their doorbell nonstop. Your analogy implies they are destroying GitHub's property, which they aren't.

Bit further than that. They're crowding your front porch with the explicit purpose of preventing any of your friends, family or customers actually getting to your front door. I think the intent is important to note. It's not a child who likes the sound of a doorbell, but an adult employed to achieve a very negative outcome.