Can anybody estimate how far from that are modern 3D printers in terms of precision?

Current SLA printers could probably do it, they have much better resolution than the typical FDM machines. SLA machines have gotten a lot cheaper in the past few years but the consumables (resin) remain expensive. And FDM printers will probably never really get significantly better than the current state of the art, there's only so much refinement you can make to squirting melted plastic out of a nozzle.

I have a cheap 300USD FDM printer and even on that you can put a 0.2mm nozzle on and use 0.04mm layer height. These sizes however are already not very practical, in addition to being excruciatingly slow to print it does a very poor job of handling any geometry with overhangs in the printed object.

Even the cheaper SLA models (i.e. Wanhao D7 is ~500USD shipped from china and a kickstarter model called SparkMaker is supposedly going to be 250USD) are capable of fantastic levels of detail.