Centaurus, as you appear to be from Australia the DAY VFR SYLLABUS applies. Elements 6.1 and 6.2 clearly state that you need to do both. It is also in 19.1 and 19.2 for the CPL. If you are running out of fuel or daylight, or whatever, you will have to convert the bounce into a landing. If you have enough runway left. If you don't have enough runway left, you must go around. I indeed would be surprise if as you state "Was surprised to find out that some flying schools do not advocate training for this manoeuvre and in fact there are a few PPL and CPL holders that have never been taught how to recover and land from a bounce. In turn it means that many instructor graduates have never done a bounced landing recovery yet they are supposed to teach students all aspects of aircraft handling near the ground. A case of the blind leading the blind, maybe?"
Have a look at that school's operations manual I think you will find that some one is just lazy and is telling you bull****. If you feel strong enough, talk to your FOI.