Is it reasonable to not publish data from research for fear of undermining previous work?
The statement you quote sounds terrible. It points in a direction where things approach the unethical. Publication of negative results are less common that positive although, I suspect, negative results ARE more common than positive. Since I am in an experimental field, I have never obtained the perfect results and always end up describing what went wrong; and I am not alone. Anyway, I think your idea of writing up your experience is good. Naturally, I cannot judge the merits of the experiences in terms of publicability.

So I think your intention is very sound and the reaction of the lead investigator suspect (or at best narrow-minded).

To me " further publications shouldn’t raise more limitations that should have been mentioned in the original publication" (if verbatim from the lead investigator and with my emphasis) sounds as if limitations were not included on purpose in the original study. So, if that is true then I can understand the nervousness. It sounds almost fraudulent.