If you don't own the home or apartment, you don't own the structure that your pet may be damaging. While you don't necessarily thing your dog or your cat smells, or think that your pet will never mark, you also dont have to pay to replace carpet when they do if you rent. You may also not be paying for just your apartment. The landlord basically takes that fee for the one or two times he has to completely recarpet or re-drywall an apartment or home because it was destroyed by pets. So yes, they can, especially if you sign a lease saying you'll pay it.
Lifelong pet owner who's rented for several years with them