I think you will find that this is incorrect - regardless of how you interpret Ch 29.
From Chapter 29:
The term “current” in existing §61.75(a) and
(b) as it relates to a foreign-pilot license is really
intended to mean that the applicant’s foreign-pilot
license and medical license have not been surrendered,
suspended, revoked, or expired, and that AFS-760 has
issued the applicant a Verification of Authenticity
letter as a result.
It also seems clear given the discussion of restrictions and limitations in Chapter 29 that these are intended to cover such things as no night flying (if that's a restriction on the underlying licence), or being restricted to certain makes and models of aircraft (in the case of our antipodean friends), etc.
When I went through this process, I checked this with a local flight school, a Designated Examiner and with the local FSDO.