I think it's a bit of both, and different breeds definitely have different temperaments and traits. There are also genetic lines in the mix with some parents coming from a line of aggressive bred dogs.
I grew up around dogs and in a very dog orientated family which firmly believed it was always the owners fault if a dog was difficult, aggressive or untrainable. And there are a lot of doggy lovers out there who seek to perpetuate this line because of their love for dogs. Which I understand but it's not helpful.
Since having my own dogs and getting to know different breeds over the years, I can say there are huge differences between breeds and even within the same breed. We have a husky mix. He has a very strong prey drive which has been very hard to train him out of. He is incredibly strong, and if he wanted to, I don't doubt he could kill another dog, maybe even a human. Luckily, we've worked hard to train him and he's incredibly loveable and soppy. He's never shown any aggression towards humans at all. He wouldn't, I believe, harm anyone. But, I do think with a large dog like that, you have to be very careful and always aware and know they always have the potential to do harm. They are animals with animal instinct.
One of our other dogs is a very small, gentle breed. I don't believe he could harm another dog even if he tried really hard! He hasn't got it in him. He also has no strength, so even our children can walk him on their own and if he pulls on the lead they will still have full control over him.
I could imagine that in the wrong hands, or with a lapse of due care and attention, when feeling threatened or otherwise provoked, many big strong dogs have the potential to do significant harm. Some breeds could do a lot of harm. And if a dog breed is specifically Cally bred for aggression or from an aggressive line, then the end result is not good.
I also do think that generally, when out walking your dog, some owners of pretty 'easy' breeds have no clue the struggles other owners go through with their often very complex and difficult to train pooches! There are a lot of judgemental dog owners out their who credit their dogs beautiful behaviour to their own talents and will look down on owners still training their dogs or who are having trouble with their dog on a particular day. While good training has a lot to do with their dogs behaviour I'm sure. The route to achieving good doggy behaviour is not the same for everyone and a little more patience and a little less judgment between owners would be nice!