The Arri Alexa refers to a native ISO of 800 but you can go to 100. The Sony A7s won't go lower than 3200 with log enabled but I think that's just protecting their other products. It's a good question, I would like to understand this too.
I'm not entirely sure about this, but I have a pretty good idea of it.
There are basically 2 possible reasons. 1. is the native sensor ISO, which is a pretty simple concept. It's basically the native ISO for the sensor, so for instance 200 for m4/3 and fuji or 100 for Canon and Nikon and much higher ones for other cinema cameras.
But in terms of video, the 'native' ISO is actually artificially deduced. Most pro cameras natively utilise something called a 'log' profile. It's basically just a flatter looking profile used to gain extra dynamic range in the shot. What it does is (I think) it raises the shadow gamma by actually raising the ISO up and then compresses the highlights to prevent blowing them out. So in short it raises the shadows, lowers and compresses the highlights, and then takes the ISO reading from the shadows. That's what I read somewhere. Now why is the Sony native ISO for Slog 1600 or so compared to V-Log's 400? I'm not sure about that, but it's to do with the way the log curve was actually developed and how it ties in with the sensor. I'm pretty sure it's not just a marketing thing.