Several considerations:

1. Never rely on what a phone agent tells you about what is essentially a legal matter. That goes for BA, BA Holidays, and Avis. However, if you call Avis, it will send you the full coverage details for your rental. You should then read those (not the summary) carefully to be certain that you have what you need. As others note, the particulars of these things change every time a contract comes up for renewal and what may have been the case for you 30 days ago for a rental at the same location, may not be the case tomorrow.

2. Be very certain that what is provided is adequate. People on FT obsess about the cost of a minor scrape, but then believed that they have full coverage when they are provided the minimum required by local -- in this case, Florida -- law. In Florida that is $10,000 per person to a maximum of $20,000 per incident. That is a pittance and can easily be eaten up in a serious accident by emergency care in the first few hours of treatment. I, by way of example, carry an "umbrella" policy with total coverage of $3 Million. The annual cost is extremely low. You may not need that, but you really need to consider what "full cover" means in your particular financial situation.