I think we're both somewhat right, somewhat wrong. _Some_ peasants -- serfs -- were considered property of their lords, or well, of the land that the lord oversaw. If they ran away, they were rounded up and brought back, usually with a beating or worse. But there were also free peasants that rented said land. I didn't really mention them, because they deliberately chose to rent said land - they _could_ have tried their luck anywhere, but they _decided_ to try their luck on this lord's lands, and so, I thought, weren't really relevant to the conversation.
But it's not exactly irrelevant, either, right? It does add to the confusion to leave it out, so, my bad.
As far as the black plague, what gave even serfs so much leverage was the fact that there were so few people in all categories around anymore. Fewer peasants to work the land, so the prices of the free peasants went up commensurately. But even serfs who wants to run far away and set themselves up as free peasants elsewhere could frequently get away with it because a) fewer men on horseback to spare to chase them down, and b) the other lord they went and rented land from didn't have enough peasants to work his land either, and had a real vested interest in making sure they weren't caught and brought back to their original lord.