In my experience "no, I was the one who was being bullied" is the classic response of the bully when the bullied tries to report. It puts the bullied on the defensive, and means they feel they will never be believed. It was one of the main reasons my DS felt he couldn't report bullying at his primary school, and didn't want me to.
The only times we were able to tackle the bullies were:
a) they were all in a car (DS, a couple of bullies, a couple of other kids) being driven by a parent where English is not their native language (to and from football), and the bullies figured that the parent wouldn't understand what they were saying. The parent didn't feel their English was strong enough to interfere and stop the bullying, but understood quite enough to be able to confirm to me that in fact it was the bullies who were bullying DS, and it was awful. Knowing this, I emailed the mother of the main one, and, guess what, he claimed that DS had bullied him. But because I had anticipated that, and had already spoken to the parent driving, and knew he would back me up, that lie was exposed.
The only other time was when one bully tried to cyberbully DS, without knowing that all emails to DS were automatically forward to me, so I just sent them straight to the parent. Again the bully (different one this time), tried to claim that DS had done it, but I had email evidence and he could produce no trace of it.
And when some bullies tried to bully DD in Year 3, again when it was reported their immediate response was that she was bullying them. As they were only Year 3, their lies weren't very good, and we were able to point out to the head that what they were claiming made no sense - they tried to bully DD becuse she had run out of class first at break and got one of the pieces of playground equipment (a tricycle) they wanted, and so they tried to pinch her, and then claimed she had pinched them first - somehow while still holding on to the tricylee in circumstances that made no sense. We were able to point this out to the head, but DD had to go through a whole inquisition about the feasibility about her pinching other kids while simultaneously on a tricycle.
I have therefore concluded from these incidents that the first and automatic response of bullies is to claim that the other person started it, even when that is physically impossible, and even when they are very young. They have worked out that this is the best way to try and level the field if accused of bullying, and put the bullied through even more hell.