He is not entirely wrong about the capacity limits of the railway stations, though. European cities struggle with inadequate railway capacity all the time.
The main problem is that the original railway stations were laid out in about 1840-1870, for much smaller passenger streams, and today find it hard to cope with modern requirements (a lot of commuters from the suburbia). But given that there is dense city infrastructure all around them, the only way to solve this is to build a new station underground, which is hideously expensive and slow.
Berlin was somewhat "lucky" to have a good place to build their new Hauptbahnhof, a result of the former division of the city. Stuttgart is rebuilding and upgrading its railway network at a great expense, the construction works started in 2010 and are far from finished.
In Prague, there is a lot of discussion what to do with the rail network in the center. You cannot just tear down whole tracts of buildings in a historical city, so yes, we will have to go the Stuttgart route and who knows what the budget (and) time overrun will be.
I commute with a train daily. The lack of capacity is visible in chronic delays, sometimes up to 30 minutes. Fortunately I do not have to be at my office at a precise hour, but going to a medical appointment without wasting too much time is already a bit of a challenge. I even witnessed a 15 minute delay at 4:30 in the morning.