Not my School and definately not my student. (Unfortunately!) I am annoyed as I know the FI involved well and he is very professional as well as being a mate. Having some amateur who heard a radio call passing judgement on his skills because of a well handled incident seems very harsh and unfair. If it had of been me, then I would be far more verbose rather than just implying you had an axe to grind.
I don't remember there having been sleet or snow on the forecast either, so if there was, then the student made a good call and the FI did a good job in having passed on enough awareness for the student to act as they did. Wx changes up here a lot and very quickly. I have sent students on flights that have had to be abandoned due to unforecast conditions, that doesn't make me a bad instructor. I don't have a cristal ball. We can only make judgements on the information presented.
There can be "politics" at this airfield between two of the operators, so I am always suspicious of of things posted on Pprune. My club isn't involved in any of this stuff and I thought all of these games had been finished with. Hopefully that is the case, but I recognise your style of writing and the backhanded way of insulting someone under the guise of "praise."