In my experience the latter Tafflyer . Most people will likely get an initial boilerplate and handful of Avios as an initial reply to a complaint, but more often than not attempts at follow-up on the part of the traveller will be met by stonewalling. Either pure silence or copy/pasting of some other ready-made corporate-speak.

Regarding the latter, I would not use the term "inability" but rather substitute "disinterest". I'm sure they have done the maths and know the "cost" of throwing Avios at the problem is cheaper than actually addressing it - assuming, of course, that BA would ever be willing to spend hard cash on fixing a problem !

I put "cost" in quotes because of course BA know they can control both the value and the redemption ability of Avios. And there too I'm sure they are keeping one eye on the big-data stats about how many people use the complaints Avios that are being thrown at them.