I wouldn't want anyone going into my apartment like that either! It was very rude of the landlord to put the pressure on you like that. How did the previous tenants wash their stuff?
A little white lie perhaps could help? Make up some story about how you let some friends use the machines and they always left a mess, "borrowed" your detergents, never cleaned the filter and so on and it ruined your friendship. Not that you think they would do something like that, but it's a risk you'd rather not take.
You know, washing room dramas have lead to murder.