Right. It's a ledger that's validated during every channel update, and monitored by third parties. To cheat you need to collude with your channel partner, and to get traffic you need to build reputation with third parties.

It's infeasible to send every deposit to the chain on close, but that isn't necessary: we just need to keep the funds and accounting inside the L3. Cooperative close requires all the deposits be first re-homed, and commitment transactions have a new overcapitalized output that's goes to a party of last resort that uses the excess to re-home everything