If you know women that have falsely claimed DV then you are an aberration because it doesn't happen a lot. Now in divorce situations you might see some women making false claims to get more out of the dad, but very few divorce lawyers are going to give credence to that or bring it up in the divorce without some sort of police report confirming the incident.
From my perspective, it probably depends on what the local laws are.
Up here in Maine, I do the majority of in-custody arraignments for my city. I'd say somewhere between 10% - 20% of domestic violence incidents are either fabricated or exaggerated. The easiest way to get a leg up in a custody or divorce case is to file a case for DV. Similarly, it's an easy way to avoid getting thrown out of your boyfriend or girlfriend's house in a breakup.
Case in point: Last week, a guy got arrested for domestic violence. The facts: he calls the police to say his girlfriend is on drugs and belligerent. She's at his home, and won't leave. She's got a criminal record, and is on probation. He's got no record. The police show up. He admits to grabbing her by the elbow and trying to escort her out of his home. She admits to punching him in the face as retaliation. She doesn't live there, and has no legal right to stay on the premises after he asks her to leave. There's no allegation of physical contact by him other than grabbing her by the elbow and trying to walk her out the door.
Guess who got charged with domestic violence? Hint: It wasn't the person who was trespassing, on drugs, on probation, and who punched the guy in the face.
I could give you probably two dozen stories that are less striking, but still show very poor judgment on the part of the police and prosecution in terms of bringing charges.
All that said, the number of actual perpetrators of DV is much, much higher than the number of false accusers. Even if only 80% to 90% of DV charges are legit in my jurisdiction, I'd guess that there are many, many more cases that aren't reported.
Also, of course, this incident isn't made up out of whole cloth. There are witnesses, and Williams admits to pulling a gun and leaving his vehicle.