I consider myself an experienced and sensible dog owner and have owned multiple rescue and one pedigree dog over the years.
Out of 7 dogs I’ve trained myself I have had two that were reactive - both rescues with very bad starts.
First one was rescued from a puppy farm, had a serious health condition as a pup which affected his mobility and was enormous, so far too big to carry everywhere. We did our best, but he ended up lacking socialisation during the most critical period and this was topped off with a really bad experience with a horrific vet who traumatised him towards people for life. No matter how much training and behavioural therapy we did we were only able to improve his fear aggression a small amount, to the point where he would ignore other people and dogs, but still panicked if approached. So, once we realised that he wasn’t making any further progress and instead just putting him in situations that stressed him out and made us all miserable, we chose to manage the situation as best we could. Identifying places and times to walk him when there was no-one else around and always going with at least two people so we could easily avoid anyone that might suddenly turn up. Sadly he died from cancer at a young age, so we will never know if he would have improved further as he got older.
Second dog we still have now. He was a rescue, but unbeknownst to us, was not only ill, but highly infectious, when we picked him up. He was dumped at less than 24 hours old, so didn’t have a mother or siblings to learn off and his illness meant that he wasn’t allowed around other dogs until he was 20 weeks old, so missed the critical socialisation period. (Actually, we were permitted to carry him out and about, as long as he didn’t come into actual contact with other dogs and we did A LOT of carrying him, even when he was so big and heavy that we would have to pass him to each other every five minutes. Again we did our best, he went everywhere from the local park and roads and into town to classic car shows and VW meets and was liberally treated in attempt to make positive associations with as many different people and situations as we could possibly manage, so he wasn’t confined to the house in isolation.)
First walk we took him on, he was literally flattened and rolled over by two large breed dogs. A few days later, while we were just getting him over that, it happened again. As a result he became fearful of off-lead dogs. He simply never learned to communicate effectively with his own species and other dogs misunderstand him as much as he does them.
He went to two lots of puppy classes and spent the first few weeks hiding, before gradually coming out, gradually gaining confidence and passing both. He learned to cope with other dogs when they are on the lead, but is terrified of off lead dogs. We have done lots of further training, including BAT and been to see three behaviourists, including one who is the leading specialist for his breed type and he’s better than he was, but will always be a work in progress (he’ll be 5 soon).
He is a bright, loving, well trained lad who is a lovely family pet, but rather more than ever-so-slightly neurotic. Part of that is down to his bad start in life, part we have been told is just who he is (he has breeds in his mix that have a tendency towards being highly strung as well). He has separation anxiety and is reactive to dogs that are running off lead and people will still allow their dogs to career up to him at full speed whilst he is barking and spinning on his lead. 
Although still nervous, he will say hello nicely to other dogs that are on the lead or loose, but plodding rather than racing around.
He is happier doing lead walks around the roads, than being in a big open space where another dog could appear any minute. Luckily we have a large garden where he can run and there is fairly local field for hire for off-lead walks without having to worry about other dogs.
My point is that some dogs don’t have the start in life that they need to be confident in every situation and it is possible for people to have a dog from a young pup, do their best to do everything right and still end up with a reactive dog.
The 5 other dogs I have trained have all be well balanced, sociable dogs with no issues. Three of those were also rescued as puppies, but had a better start overall. One was a pedigree that we checked out everything really carefully for before we got her, including the temperaments of both her maternal and paternal lines. We also chose a breeder that started socialisation early and was highly proactive in making sure all her pups were well rounded, with good temperaments and matched to the right owners. She was an awesome dog, trained to a very high standard and brilliant with every man, beast and child she ever met, but then she had luck, breeding and the right start on her side.
I am a huge fan of rescuing dogs, but having had two with such major problems, I am thinking if I ever have another I will probably go for another pedigree with a similar background to my old girl, because I miss being able to go on enjoyable dog walks wherever I want and dogs like my boy require a huge investment of time, effort and emotion over and above your average relaxed, friendly pooch that I don’t feel I will be up to again for a loooong time.