I think it may be less to do with being fair to the neighbour and more to do with being in compliance with Part E of the Building Regulations, Sound, which is the law.
http://www.environ.ie/en/Publications/DevelopmentandHousing/BuildingStandards/FileDownLoad,1646,en.pdf (Technical Guidance Document E is here).
The appearance of a non-concrete substrate beneath the floor finish gives cause for concern.
I strongly advise that you have the building inspected by a competent building professional to ensure it is in compliance with its Fire Cert and the Building Regulations.
ONQ.
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All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.