I don't follow the page, so I am speaking in general principles here.
If the mother is vaccinated, it's likely the puppy will have meaningful maternal immunity. One of the reasons for a series of vaccinations is that maternal immunity tapers off at a different rate in every puppy. The aim is to catch the point it tapers off with one of them, so that the window when the puppy is unprotected is as short as possible.
The initial socialisation window closes by 12-16 weeks and, if you don't get the pup out at all until after their last vaccine, you miss most of that window. Far more young dogs die due to euthanasia on behavioural grounds than to infectious diseases.
So there's a tradeoff between early socialisation and not exposing them to disease risk. Everyone will manage that tradeoff differently, taking into account breed temperament, local environment, local disease levels, and owner appetite for risk. A low trafficked field in the lake district has a different risk profile from a busy park that gets hundreds of dogs a day, and different again from an area with stagnant water with a heavy rat population.
I personally socialise early, getting my pups out and exploring well before the 12 week point. I'm not saying that's right for everyone, and there are other solutions (e.g. carrying the puppy everywhere), but it's what I have decided is right for me and mine.
There's an American paper at https://avsab.org/wp-content/uploads/2018/03/Puppy_Socialization_Position_Statement_Download_-_10-3-14.pdf which looks at this in the context of puppy classes pre-vaccination
I'm assuming they have an open page since you're following them. Why not ask them, not us, for their reasoning?