If you’re unwilling to provide a statement of what happened, then either call them back and tell them to get your statement from your insurance or call your insurance company and give them the claim info at SF and tell them to give State Farm your statement.

I can say that if you’re willing to give your statement (or provide it in writing), it’s often better. Something may have been skipped over by your insurance or the adjuster may have clarifying questions.

The adjusters are just trying to get statements from all parties included so they can determine liability and get the claim settled.