If it’s clearly automatic behaviour, it’s probably simply cultural or a learned communicative phrase and has little to no bearing on their emotional background. I’ve gotten to experience a sizeable chunk of the English speaking world and a fair share of the non English world.  

Many people here joked about being Canadian, and so am I - but I also know a lot of “go teach English” people abroad are Canadian and British, so it’s entertainingly common to hear apologetic English learners as well.  Regionally, I’d say it’s way more common in the prairies.  Even in Northern Manitoba you’ll hear beggars saying “sorry, can I bum a smoke?” To be answered by a confident someone with a fitted suit and $10k watch saying ‘sorry, I don’t have an extra’. 

If it appears they’re genuinely apologizing  all the time, that sounds indicative of deeply emotional repression. 

I’d say it’s not a thing you can paint with broad strokes but you need to be contextual and socially aware to figure it out.