Diple- the Journal fact check is also bollocks and wrong.
The Taioseach as said spoke in reference to the Single European Sky programme which is specifically concerned with helping rationalise ATC control over the EU, Norway and Switzerland under Eurocontrol. Note that neither Norway or Switzerland are in the EU and EUROCONTROL is not an EU body. UK control over the Shanwick area is delegated to the UK by ICAO - not the EU.
The programme has nothing to do with overflight rights - and leaving the EU will in no way affect the control of air traffic over the UK FIR and Shanwick Oceanic Area or permit Eire or the EU to anyway limit UK overflight rights.
The Taoiseach made a threat based upon a total misunderstanding of how international air traffic and ATC is legislated and controlled, as opposed to EU licensing and landing rights under Open Skies etc - and the Journal is equally as confused.