In one recent workshop, I was talking to someone about her model, and as I gestured toward a brick, she exclaimed, in a joking but firm way, "Don't touch my model!" And I didn't. I've seen people reluctantly take apart one of their models so they could use the bricks for the next model. I've had people ask anxiously, once they've collaborated on a shared model, "Are you going to take that apart now?" Nope, I don't dismantle a shared model in front of the people who made it, because all of these things are manifestations of the OWNERSHIP people feel in their Lego® Serious Play® models.
We usually think of ownership in terms of the law, and sometimes in terms of claiming responsibility. But a sense of ownership derives from more than law: it encompasses intimate knowledge and identity. Intimate knowledge, in the sense of "I know every nook and cranny of my rental house even if my name isn't on the title" or "To open my front door lock, you have to jiggle the key just so." Identity, in the sense of "This car, which I haven't paid off yet, says a lot about who I am as a person." Think of all the things you don't legally own but you do "own" in these other senses. People who build with me don't legally own the bricks, but they do have intimate knowledge of the models they built, and they can identify with them strongly.
A sense of ownership is critical in moving on to implementing a solution--if people don't believe in it, if they aren't invested in it, they can find many ways, subtle and not-so-subtle, to resist its execution. So when I heard "Don't touch my model!" from that person, it was a good thing--it means she'll be invested in the solutions she builds.