In reply to Morts:
I've had recent experience with the insurance component of the AAC. While they've been great in terms of actually paying without argument, they were a nightmare to deal with. I spent five days trying to get them to talk to the hospital I was in and get them to send the hospital the form that I needed to fill out so they could process everything. Five days of sitting in the middle while immobile in a hospital bed, not quite understanding why they couldn't just pick up the phone and call the hospital office directly. The hospital lady was equally exasperated with them.
More recently I've been told that they won't reimburse any expenses I paid for up-front unless I 'first submit all invoices to my social health insurance' in the UK, and that once I've done that and ascertained that my 'social health insurance' won't pay, all invoices needed to be posted to Germany. I mean that's mostly reasonable...but it's not what the other person in the office said last week!
TL;DR: they do what they say on the tin, no concerns, but they're apparently an organisational nightmare.