Andrew, you might not believe it, but that doesn't make it any less of a fact.
See question 379 of
http://av-info.faa.gov/data/640otherfaq/pt61-18.pdf, page 96 (of a cool 354).
The basic rationale seems to be that a PIC excersing the rights of a US pilot certificate must have a BFR and that what is issued on the basis of the JAR PPL is a US pilot certificate.