What the adjuster's job actually is
To resolve claims quickly and cheaply. That is not a criticism — it is the role, and most adjusters do it courteously. But the pleasantness of the interaction says nothing about the adequacy of the offer.
A first offer that arrives before your treatment has finished is not a valuation. It is an attempt to close the file before the cost is known.
What you are and are not obliged to do
You must generally cooperate with your own insurer under the terms of your policy. You are not obliged to give a recorded statement to the other side's insurer, and you are not obliged to sign a blanket medical authorisation for them.
A broad authorisation lets them go through your entire medical history looking for a pre-existing condition to attribute your symptoms to. Providing records relevant to this injury is reasonable; handing over everything is not.
The four things not to say
“I'm fine” — said reflexively, quoted permanently. “I think it was about…” — speculation becomes a commitment. “I don't need a lawyer for this” — signals what your claim is worth to them. Any figure at all, before you know the medical picture.
Put it in writing
Ask the adjuster to confirm in email what they have told you on the phone. Requests, deadlines and offers all become clearer when someone has to write them down, and you end up with a record.
Confirm who you are speaking to
Name, company, claim number, and which party they represent. Write it down.
Give only the basics initially
Date, location, vehicles or premises involved, the fact that you are receiving treatment.
Decline the recorded statement politely
“I'd rather not do that today” is a complete answer.
Wait for treatment to stabilise before discussing value
Before that, nobody knows the number — including you.