And that big ticket item needing to be replaced eventually is factored into the amount of rent they are charging you as well. You are essentially as he said paying their upkeep / maintenance and building 0 equity that way.
There are definitely arguments to be made for renting over buying. Primarily if you're moving in the short term, or if you are able to rent a place for significantly cheaper than you would buy (if you are investing that money at least). Where I live you're looking at ~1400/month to rent a single family home on the low end though versus being able to buy something for ~180K at ~1200/month including PMI, property taxes, insurance. The second option is not only cheaper but also builds ~$300/month in equity in the home. I'd love to hear how renting is superior to buying in a case like this?