Why is a Plasma bridge/chain secure.

From EthHub – Plasma:

These side chains periodically report back to the main chain and use it to settle any disputes (almost like a higher court).

My understanding is that the state is stored on the plasma chain – kinda like a sidechain. But unlike a sidechain, plasma publishes the root of a block periodically.

"How do the publish-checkpoints imply plasma's security? To me it seems more like it's just notifying the mainnet of state changes.

Thanks!