Should Monsanto be able to own the rights to seed produced from seed bought from them?

Exactly - it would lead to a monopoly. But most people don't care because they don't grow their own veggies or fruit.

The even bigger problem is what if you buy seeds from a company like Burpee and then years down the line it is shown that these Burpee seeds are somehow related to Monsanto. Monsanto could go after Burpee and maybe even the consumers who have bought these seeds in much the same way that the recording industry went after people downloading music.

I'm sure the Supreme Court will find for Monsanto. They don't care about the ramifications. They'll say it's not their job to consider that and it's just their job to interpret the laws. And they are right. But if they do find in favor of Monsanto, then that means our representatives need to amend or create some new laws. Sorry, but that is how this works. And we know our reps won't do that because then Monsanto may not give them financial help in the next election.

Monsanto are EVIL. They not only want what you said but also to make illegal to possess any kind of seeds that aren't sold by them all in the name of food "safety"...

Is the issue monopolistic practices, or is it just patent law as your question suggests? Oversimplify much? Are you home schooled?