MLB rights in a nutshell:
1) The individual clubs own exclusive rights to all games in their designated blackout areas. All of them sell their rights to regional/national sports networks on an exclusive basis for a large wad of cash.
2) For all viewers in North America that are not in a blackout area, the MLB owns the rights. They sell most of the Saturday games to Fox, and the Sunday evening game to ESPN. They also sell all the postseason games to TBS, Fox, etc.
3) For anything not covered in the above, the MLB will sell direct to viewers through the Extra Innings packages on cable/satellite operators, and over the internet through MLB.tv
So here's how you're supposed to watch MLB Baseball.
If you're local to the team: You go to the game, or buy a cable/sat subscription to watch it on the appropriate RSN. They paid good money to get exclusive rights, so you're going to pay them good money in turn.
If you're not local to the team but are in NA: You buy Extra Innings/MLB.tv. If it's Saturday or Sunday, you watch it on TV. If Fox isn't showing the game you want, well that's Fox being dumb.
If you're not in NA: Buy MLB.tv, watch everything.