In reply to tehmarks:
I guess it depends on the country, in France IIRC there are several levels of doctors even within the state (EHIC covered) system, your 20% not from the EHIC could have been either just the normal patient surcharge per day that is even for locals, or it might have been a private hospital that is still inside the state system, but only partly. Probably worth checking the NHS advice on different countries, anyway:
https://www.nhs.uk/using-the-nhs/healthcare-abroad/healthcare-when-travelli...
I am still a member of the AAC and renew every year, since it's essentially "free" after a week or so because of the hut cost savings (which you would get from the reciprocity add-on with BMC). For trips outside the EHIC and higher elevations, I can also get a 500 000€ medical coverage premium for 54€ for a month trip (although the rescue costs are I think still capped at 25 000€, which could be a bit limiting in some circumstances), and from what I heard (fortunately never had the "opportunity" to check myself!), the alpine rescue services just see the card and are happy. Still, glad that everything worked out for you
Post edited at 17:25