Dear IO540,
This was confirmed by one of our Belgian IFR students. When he bought his brand new Cirrus 22, he had to get a foreign-based FAA PPL in order to fly it in Belgium.
I did not look at any information about that because I had no interest for that at this time, but if you wish I can check, that is an interesting point.
I would say that Belgium might be able to do that only for all pilots that hold a JAA PPL issued by them. I do not think it is linked to citizenship, but depends on the issuance of the license.
In some other countries it is the exact opposite : see Monaco for example, you can fly VFR or IFR on their national-registered airplanes with your FAA license, without having to get a local license.
In fact, countries have full authority on which licenses they accept to fly their own airplanes, or which airplane can be flown with their own licenses (at least over their country).
But if they are very hard, the other country can apply reciprocity on rights.... and limits.
Amivolement,
Alexandra
ORBIFLY