It was Suncorp (I believe AAMI are owned by Suncorp) insurance.
We had a claim recently and they wanted to know if we were happy with the work. Good of them to follow it up.

Tim... you are so right.

It's definitely Aami they rang me (I had a car accident and had lodged a claim with them) and since I missed the call on my mobile they rang my house number straight after and said they'd just called me. So it is definitely Aami insurance :)

This is a generic phone number which comes out on outbound calls from a Suncorp Call Centre. For example anyone from their business or insurance division calls you, this is the number that you will see. If my friend who works there calls me from her direct line, this is the number that comes up.
Often you will receive a different number to return the call which is the person"s direct line.

When I answered, nobody replied.

Looks like (07) 3330 0000 can't receive calls, I had a call from them (Suncorp) and the bloke advised me to call back on a different number. This one was legitimate, no scam.

I also recieved a call from (07) 3330 0000.  No idea who it is.  Googled the number to find out (was excited and thought I might have won a Competition prize.. doesn't look this way now

For me, this was GIO finalising my claim and my settlement. So a nice call to receive.

Same as Jacob, AAMI service centre

Nothing dodgy - and no, they are not suss of your claim.