  We refine a result of Matei and Meyer on stable sampling and stable
interpolation for simple model sets. Our setting is model sets in locally
compact abelian groups and Fourier analysis of unbounded complex Radon measures
as developed by Argabright and de Lamadrid. This leads to a refined version of
the underlying model set duality between sampling and interpolation. For rather
general model sets, our methods also yield an elementary proof of stable
sampling and stable interpolation sufficiently far away from the critical
density, which is based on the Poisson Summation Formula.
