No further action doesn't mean it isn't true or didn't happen. Domestic abuse is very difficult to prove/evidence as it most commonly happens within the home environment with no witnesses/CCTV or other "tangible" evidence.
Not all domestic abuse is physical either, but even in cases where there are injuries it can be difficult for charges to be made.
I work in this area OP. I've also a victim of domestic violence.
My ex husband held a knife to my throat in front of my daughter. He threatened to kill me. Police came and took him away at the time but there was no further action due to lack of evidence. I had no physical injury, he said in interview he didn't do it. It was essentially one word against another so it went no where.
That is just one example, there were many other occasions before this.
He's now with a woman who has two young children. I bet he's told her that false allegations were made against him. It's what they do. I know he's said I'm mentally unstable (I'm not. I work in a job that requires me to be very mentally stable). It's DARVO like PP said.
PP has got it spot on- he's trying to do the "nice, honest" guy thing by coming across as "upfront" about it. It's so when you are told, you've already got his story in your head where he is the victim, which will make it difficult to believe anything you are told and i you will discount it.