@Anna Watkins If they are the original hardwood floors most likely the finish that was on them has worn down enough that the hardwood itself maybe easily damaged by the amount of water from the steam cleaner. In any case, liquid and hardwood does not mix if the liquid is given time to penetrate the wood. Cleaning/wetting the carpet that is sitting on the wood can cause the boards to ripple or if enough water penetrates, buckle. If the unit is a rental and you don't want to spend the money to refinish the floors, sometimes you can get away with a buff and coat, depending on if any other contaminants have been sitting on the finish, such as floors being previously waxed or furniture polish that has remained on the floor when the previous owners were cleaning their furniture. My recommendation would be to have a hardwood flooring contractor give you an estimate to see if the cost fits your budget.
If the flooring underneath is laminate, you might as well call it a day if you decide to steam clean your carpet. Laminate flooring is like a sponge and will easily absorb water at its seems.
The finish on most engineered flooring is extremely durable and really protects the wood itself. That being said, if the carpet is not properly steamed with minimal water left behind, the potential for damaging them is still likely.
If you have any other questions, please let me know. My family has been in the hardwood flooring business for more than 30 years. I myself have worked with them for over 15 years.
In my experience with renting carpet cleaners is they usually leak. Some of them leak a lot so be careful.