The actual theoretical knowledge requirement is:
Meet the knowledge requirements for the grant of
a JAR-FCL Commercial Pilot Licence
(Aeroplanes) as per AMC FCL 1.470(b).
A FAA CPL does not meet this requirement. Neither do any of the other qualifications to which you refer.
Although the PPL(A) is a non-professional JAA licence, those conducting flight instruction for the licence are required to have at least JAA professional levels of knowledge.
Many in the PPL training industry consider this excessive and wish to change the theoretical knowledge requirements; this may be achieved eventually, but not in the immediate future.