We study the conservation of observability after sampling for the class of switched linear systems with no inputs and switching in the measurement equation only. Using van der Waerden's Theorem, a classic result from Ramsey Theory, we give a sufficient condition on the components of the resulting discretized switched linear system for it to be observable under arbitrary switching sequences. This preliminary result then enables us to extend the Kalman-Bertram criterion for nonpathological sampling to the class of switched linear systems under consideration.