You read correctly, except these rules apply only to "native" caravans -e.g. those in Spain carry two number plates - one as the car and the second for the van itself. Viting caravans do not need other than their own national plates.
However, things are not quite so straightforward with other regulations. Currently there is considerable debate about whether outfits with an overall length of more than 12m visitng Spain require the Spanish version of "long vehicle" plates.
UK Caravan Club seems to think they do, although are not very specific. German automobile club also thinks they do; Dutch seem to think that "home" rules apply, which appear to mean that Dutch outfits have to be 18m. long before needing such plates. The logic is that "home" rules of an EEC member country apply wherever, but this does not fit with the need for us to fit headlamp deflectors.
So if your outfit is less than 12m overall, and you have beam benders fitted, i should not worry too much. Get CC Europe site guides which have generally good advice about what is required, despite being a bit vague in some areas.
The bad news is that if you get unlucky, most European countries now levy spot fines with a discount for paying on the spot, but that argueing can be very inconvenient and double the fine. And we were told that EEC meant common rules and open borders - dream on.