I think our parents' generation either have a very rosy-tinged remembrance of our own childhood days, or they're barefaced liars!
It's definitely true that people used to potty train a lot earlier. But then nappies were either cloth, or expensive disposable, and there was every incentive to train early. I think it was also a cultural thing in those days - everyone had an expectation that babies would be out of nappies well before they were two.
My own MIL claims that because there was only a year between DH and SIL, when she came to train DH at about 2, she did SIL (11 months) at the same time. TBH, I actually don't believe her, or at least, I don't believe that it was quick and wholly successful. I've borne the brunt of a lot of pointed comments from her about how late we left it with DS1 (he was extremely resistant to the whole idea until nearly three and a half, and is still having the odd relapse at 3.10). My mum also thinks we should have 'done' him sooner, but she's better at biting her tongue!
Anyway, we waited until we thought DS1 was receptive to the idea, about 3.2, and went cold turkey, a la GF, and in line with the Mumsnet Rules.
It was an unnmitigated disaster and I think it put DS1 off the whole idea for months. After I'd started, I realised that going cold turkey completely went against all my other parenting decisions. I'm quite lentil weavy attachmenty; I bf on demand and until my boobs dropped off DS1 wanted to stop; I've never done CC. But sticking DS1 into big boy pants and then taking him to the loo every 15 minutes, often against his will because he was too busy or didn't need to pee.
Not very child-led and it went against my better judgement. Yet I'm not sure if potty training can always be child-led. Some children just don't seem to want to get involved and need some sort of coercion. We gently tried again at about 3.5 and this time, he was ready and took to it brilliantly. As I say, he still lapses, either because of illness or just because he's bored of it, I think. And most annoyingly, he started off by being completely dry in his nappy at nights, but after his first relapse he went back to soaking a nappy at night. 
DS2 is in cloth nappies in a desperate bid to make him aware of what being wet feels like. 
It's a confusing and often stressful path for both child and parent, potty training. I'd do whatever it takes to make it less stressy. There's an Elizabeth Pantley book (she of the NCSS) for those who like her sort of approach.