WE have used Tiffany Towncar 4 times now with our son and each time they provided a nice car seat. This last time it was more of a booster as he is nearing 40 pounds. In fact, they asked which type would be better. TJMW2727 - that is too bad that they didn't do this for you.
Keep in mind, that Florida law states that those using public transportation do not have to have children in car seats. This includes cabs, shuttles, hired vans, limos, buses, etc. If the cab driver makes you have one, it is by his own choosing. We had this discussion with Tiffany on one trip and that is what we were told.
That being said, I no longer count on car seats from rental companies. They are horrible. Not very clean and hard to get into the car to fasten properly. They are the cheapest you can possibly buy. And, often they won't guarantee you that they will have one. The one and only time we used one from the rental we had to wait 1/2 hour for it...and then we went right to a store and bought a new one. Couldn't leave him in the one they had.
You can check the car seat just like luggage. Most airlines don't count it as a piece of luggage. You can also bring it to the gate, and may be able to use it on the plane, if there is a seat and you haven't bought a ticket. If not, they will gate check it for you.
But in answer to your question -- BRING YOUR OWN!!! Then you know for sure that you have a good one and you know where it has been.