Depends on the state. Some states are tenant friendly, others are not. If the landlord is able to rent the apartment out quickly, he might not have any real damages so suing you might be a waste of time.
Legally yes a tenant is liable.. but there isn't a court that is going to enforce a residential lease, if the teneant has moved out and surrendered the security deposit a court is not going to find that the tenant must pay the remainder of the lease...
Yes, technically the tenant is responsible for it, but in reality no court is going to find in the landlords favor, and it is a waste of their time and money to sue over it... because they will lose...
Its a nice threat by landlords, but in reality it rarely ever happens that tehy win a judgement under those conditions in all 50 state.s