I am a much simpler man than some of the evidently big brains who have posted already so despite my experience and age I've found this thread educational but in a way a little inconclusive.
I have been often baffled by the desire of other pilots (usually with little experience on type) to try and hand fly the jet on the glideslope when visual sometimes below minima. Surely it is easier to look out? I note from other posts that the PAPIs aren't terribly accurate and will likely be set to result in touchdown further down the runway than the G/S but I would advocate having an aiming point on the runway which should not move up or down the windshield, isn't that one purpose of the runway markings also discussed above?
In sympathy with the OP's Trainer, maybe (s)he was concerned that once you get to 4 reds and maybe aren't looking at the G/S anymore, then how do you know how much below the 3deg slope you are? I'd be doubtful too about the accuracy of data monitoring information the OP has referred to. What is the sample rate apart from anything else? The trainer has at least succeeded in getting you to think about your technique.
Standing by to be torn apart.