I agree, I think that all dogs can have separation issues but you can train them to be able to be left. Are you thinking of a puppy? That would be easiest in terms of training to be left I think, rather than a rescue. NOT saying don't get a rescue (!), just commenting for this specific question.
Don't be too scared by the internet etc. There's all manner of scare stories.
We got our Springer nearly a year ago now, from a puppy, he's our first dog. When we said we were considering a Springer, most people thought we were daft, as most Springer's they knew were 'nutters' and would tear up our house if not given 10000 hours of exercise a day. Dogstrust told me they wouldn't rehome this breed as they were not an ideal first dog.
Our dog is nothing of the sort! I have no idea if it's just temperament or the fact we take training and walking him seriously, but he's been a dream, he really has. The internet said much the same in terms of separation anxiety etc, true, he likes being near us if we are in and will tootle behind me where ever I go, but he's fine being left.
He's not been walked for four days now as he has a poorly paw and he's just as chilled as ever. I did notice though that, when he went back to our breeder, who had him when we went away at half term (non uk, he comes with us otherwise), he was far far busier and needed a lot of consistency to re-establish the 'rules'. Her house is chaos though, as she's a child minder and curtain maker too, and more relaxed re training, being upstairs, on sofa's etc. which made me wonder about 'nature and nurture' a bit tbh.
The thread is interesting though, as I have just agreed to another puppy, a GSP 