Certainly true, to an extent, in Copenhagen, which was car-centric before they sarted turning it around in the late 70s - though not 'just' infrastructure per se, also things like the green wave, and street layout that wasn't intended to separate cyclists or make it safer, but rather make the car more inconvenient, which then got people onto bikes etc etc.
Not so much in the Netherlands where the infrastructure just followed the fact that so many Dutch already cycled. They maintained that culture right the way through in spite of a lack of segregated lanes and so on - so the tolerance was already there then they thought, why not make it even easier since so many already cycle. And again a lot of the encouragement to cycle isn't necessarily in safety infrastructure, but in the likes of the massive conveniently placed bike parks that sit closer to the railway stations (for example) than car parking.
So many shades of grey as to why there are so many cyclists, can't be put down to one cause, and the primary causes will be different in different locations.
What IS clear is that in the UK both the safety infrastructure, the 'other' infrastructure (I mean, bike parking on George Street is abysmal), and driver culture, ALL has to change. Some will feed the others, but there's an interplay to it all, which is generally why trying only one and expecting it to be the magic bullet never works.