I would love to know the legalities involved here. Is it illegal to receive any stream that originates outside the United States?
Not any stream, only content that isn't licenced for streaming in the US. An example like this would be a UFC PPV feed from SKY Sports that I often see streamed. That's not licensed for use outside of the UK, and any stream into the US would be illegal that wasn't authorized by the UFC. The key is UFC is the copyright holder, and those rights extend to dish (or any pay tv provider that has an agreement with the UFC) via licensing of its content. Now, if the UFC authorized an overseas streamer to stream its PPV on the internet for free, then that would be ok as they have permission from the copyright holder for fair use through a licensing deal. (Unlikely) If that happened it would be fair game, but in reality, we know that's not the case because the pay tv providers have those agreements for PPV.
Also, If it's originally produced content not under any type of license or fair use is ok. Anyone who produces content and owns the rights to it can stream it anywhere as prohibited by regional laws. If I wanted to go out and produce my own porn, I have every right to stream it on the web, but it would be my legal duty to block middle eastern countries that have a ban on pornography to meet their laws under international law.
Streaming a whole PPV or movie isn't considered fair use and harms the TV providers who do pay a license to distribute the content and is harmed by this as their PPV revenue is decreased because people won't buy it if they can get an internet stream for free. The KODI stick has made it easy for anyone to pick up these illegal streams that aren't fair use, licensed, or even authorized for distribution over the internet.
What Dish and I suspect AT&T will join at a later date, is fighting against this as it's a form of piracy because the content that the KODI sticks are putting out via it's plugins are essentially giving away programming that isn't free and dish pays the content providers a fee for carriage of that programming (licence agreement). Also, the streamers who are putting it on the web don't have the rights to do so and that in itself is also illegal.
The other factor is content is licensed regionally and cerin programs are available in the US that isn't in the UK, Asia, ect. One program may be PPV here, but free in the Middle East, intended for the Middle Eastern market only as a freebie but full outright PPV here.