We show that results in Ergin & Sonmez 2008, that for schools it is dominant strategy to truthfully rank the students under the Boston Mechanism, and that Nash Equilibrium outcomes in undominated strategy of the induced game are stable, rely crucially two assumptions. First, (a) that even when able to manipulate how students are ranked, schools need to be restricted to find all students acceptable, and (b) that students cannot observe the priorities set by the schools before submitting their preferences. We show that relaxing either assumption eliminates the strategy dominance, and that Nash Equilibrium outcomes in undominated strategies for the simultaneous induced game in case (a) and Subgame Perfect Nash Equilibria in case (b) may contain unstable matchings.