The idea of the hoverslam is to arrive at zero vertical velocity at exactly zero altitude. This is complicated, but can be done fairly reliably when "zero altitude" is stationary - on land landings or drone ship in calm seas. In heavy seas as today, the drone ship deck is pitching up and down, and it's really hard to predict the altitude it will be at the exact moment of touchdown. If I had to guess, I'd say the calculations are done against the highest possible or average position of the deck, and during today's landing it was at its lowest point at the moment of arrival, causing the stage to drop the last meter or so. This is what the crush cores in the landing legs are for :)
But oil rigs aren't easily movable, and they will want to get the rocket back to land. I suppose they could crane it across onto a drone ship barge, but landing directly on the barge in the first place seems to be working out ok so far and saves a huge amount of extra cost, time and trouble.
It's not about having anchors, it's about not being affected by the top layer of water which moves up and down due to waves. If you submerge (your center of gravity) just a few meters under the surface, you'll suddenly be much more stable and much less affected by the waves. Oil rigs, just like ice bergs, have a large part that is submerged and invisible on the surface. Look at this for example: https://s-media-cache-ak0.pinimg.com/736x/73/64/d6/7364d6da3...
The problem with a rig is all that vertical structure. It limits where the vessel can be towed to for offloading. To get this rocket off, they need a regular commercial dock.
I'm pretty sure they already flood the ballast tanks for stability.
