I'm from Spain and I spent a couple of years living in the UK, and I think "the stories of Spaniards about our superior drinking culture" are actually very true. Mind you, I'm not a chauvinist, there are very few things where Spain can give the UK any lesson - but this, I think, is one.
Yes, alcohol consumption per capita is probably larger in Spain than in the UK, but people mostly know their limits. The transition from social/family drinking to "botellón" is smoother than the typical all-or-nothing transition in the UK. The fact that it's more socially accepted also means that people talk about drinking in a casual way, that your friends or even your family will advise you, etc., so it's much rarer to actually get into serious health problems or become an alcoholic.
I was a rather hardcore "botellón"-goer in the 2000s (I think "peak booze" in Spain was more or less in the same date as in the UK), most of my friends were too, and the largest problems anyone had were maybe throwing up and passing out once or twice in 5-10 years of partying. In the UK on the other hand, I met people who drank way less frequently, but the day they did, 90% of the time they weren't able to walk home on their own. It was even worse when they passed some stupid law forcing pubs to stop serving alcohol after 11 pm - some people would gobble up as much booze as they could right before that time, and in less than an hour they would be unconscious.
In general, in all the places where I've been, the pattern is the same: in places where alcohol is socially accepted (Spain, Italy, Germany, Greece) I've seen fewer problems with alcohol than in places where it is frowned upon (UK, Sweden, US).
In fact, you can even see it inside Spain itself... what nationality are the people who practice "balconing" (getting drunk and jumping off from a balcony or window, often leading to death)? An overwhelming majority of British, with the odd German here and there.