Should I give a recorded statement to the insurance company?

NO! Although the adjuster may be nice to you and seem like he wants to help you, it is actually just the opposite. 

We do not recommend giving a recorded statement to the insurance company.  The questions the adjuster asks you are meant to trick you or they will try to twist your words to get you to say something you don't mean to say. 

They may tell you that they are "just trying to gather information" or that they "cannot settle your case without a recorded statement."  The purpose of a recorded statement is to lock you into a story, usually before you get an attorney, so that if your story changes later on, they can use the inconsistencies against you.

Insurance adjusters are highly trained professionals with extensive experience in taking statements from injured people.  They are not trying to help you.  They are trying to determine your injuries and damages early in the case and minimize how much they have to pay you.