I would say it looks more like tail biting. I had a betta that got his tail stuck in the filter, and only the webbing in between the rays was lost, similar to a crowntail. The roundish chunks on your betta's tail usually gives it away as tail biting. And as for nobody seeing him in the act, remember, he could do that damage in 4 seconds flat! One second there, another second gone.
Anyway, I have had a lot of fin regrowth problems because my water is hard and my betta's tail is so big and delicate, so I'll give you some tips for fast regrowth. Definitely keep the water really clean, like you mentioned. I do daily water changes when I'm trying to regrow fins. I put the water up to 81 degrees to pump up his immune system a bit. Stress coat to condition the water, and just a little bit of salt really help. Stay away from Bettafix/Melafix, even though people do have success with fin growth from it. It's not good for betta's lungs and is very dangerous. Also, I give mine one extra pellet or bloodworm in the evening because the protein helps.
You should see new fin growth in 4 days. It's smooth and clearish white. Hope I could help! Good luck.