I'm not sure what part of the aerodrome operator's comments you believe are false. You don't mention a reason behind their decision to close the aerodrome or that they said they have to close due to works. They might just feel that the risk is too high so they will close down the whole aerodrome.
You and others are correct that there are plenty of ways of managing the risk of aerodrome works to keep and aerodrome open - displaced thresholds, NOTAMs, Works Safety Officers, etc.
But your comments regarding taxiing aircraft infringing the splay aren't accurate for compliant aerodromes. If a taxi route traverses an area "downwind" of a landing threshold, the holding position should be set back such that the holding/taxiing aircraft does not infringe the approach surface (splay). If you were referring to the transitional surfaces (off to the side of the runway), then some aircraft may infringe this surface if the geometry is right (or wrong, depending on your point of view).
Others' comments about OLSs, IAPs and specific operational impacts are little off too. Firstly, certified aerodrome operators are required to establish and monitor the OLS. Maintaining clearances is a little more of a tricky game sometimes. There are plenty of temporary and permanent infringements of OLSs at Aussie aerodromes and the accepted mitigation appears to be displaced threshold, marking, lighting, NOTAM, ERSA or a combination of these. IAPs are a different case with objects assessed against PANS-OPS by the IAP designer and mitigation here will end to be a lifting of minima or other operational restriction.