We are not located in Florida but instead located in Michigan and we have been asked the very same question.  In Michigan this is also not a document that is not normally recorded in the register of deeds office but instead is only in the court records of the county, and IF one of these documents even exists for the parties in question in the court records.  The only time we will do this type of search is by a separate request at an additional fee whether it's for Altisource or any other company as we only search the real estate records of the county and not the court records.  The statement  "no searching has been performed in the court records" along with other disclosures of this nature are right on our write up forms so that all clients know what is being searched at the time of their request.  By putting these type of disclosures on the write up forms reduces any type of liability on the searcher(s) as you told them what you did right up front.  We too have said to clients that this is not something we do unless you let us invoice you separately.  In some counties, as well, the court systems can be many miles away from the actual county building so it's not like you can do it even the same day as the court offices have different days and hours of operation than the real estate records department. 

Any questions, please feel free to call our office or email us directly.