I think there's something to this, but I've never personally tested it because I've always gotten my dogs as either young (9 & 10 weeks) or older (16 & 20 weeks) puppies. At home training has always been almost entirely off leash, and we start taking them to off leash parks at a fairly young age - around 4 months for Dena & Keefer, and Halo at 15 weeks old.
When young, I think especially in a new environment away from home, there's a natural inclination for the puppy to stay close and follow the owner. Having this be a normal routine part of their lives from an early age makes it no big deal, as opposed to a dog being off leash for the first time as an adult, where it's a sudden novelty.
Still, my dogs are never off leash around roads and cars, we only take them to safe off leash areas. And I would never leave a dog loose if I didn't have a fenced yard either. Better safe than sorry. And as you said, consistent training is important too.