In landlord/tenant disputes like this, it is usually the landlord side that is more aware of the legal rights and responsibilities of each side of the contract, and can win the argument if it comes to a contest. In addition, the rental contract is usually tilted toward the landlord in ways the tenant may not even know about.
However, it is better to meet with the tenant, show them the lease, remind them of their obligations, possible future legal and credit problems they could be facing, and then come to a compromise agreement. This way they are far more likely to remove all their stuff, clean up the place, and hand over the keys (formal surrender of the premises). Helps to remind them that if they do all the right things, they may get some of their deposit back or forego damage to their credit. It all goes back to the written agreement that governs your relationship, an alien concept to many tenants.
To really insure you two are on the same page, put your new understanding down on paper, which is legally an ammendment to your contract. I always keep a tablet with carbon paper for such an occassion. If you are under 30, ask anyone over 50 what carbon paper is.
